Finite Group Databasebeta

← Group #72271532

Character table — Group #72271532

Order 1536.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102
size1111222222222244444444444444444488888888888812121212161616161616161616161616161616161616161616161616161616161616161616161616242424242424484848484848484848484848
order124422234446121244446668888888812121212121212242424242424242422442244446666881212121212121212161616162424242448484848484848484488882444448816161616
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111-11-11111-1-1-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111111111-11-11-1-1-1-11111-1-111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111-1-111-1-111-1-1-1-1
χ4111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111111111-1-1-1-1-1-1-1-11111
χ511111111111111111111111111111111111111111111-1-1-1-1111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ611111111111111111111111111111111111111111111-1-1-1-11-11-11111-1-1-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1111111
χ711111111111111111111111111111111111111111111-1-1-1-1-11-11-1-1-1-11111-1-111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-11111
χ811111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-111111111-1-1-1-1
χ911111111111111-1-1-1-1111-1-1-1-11111111-1-1-1-111-1-1-1-11111111111-1-11111-1-11111-1-1-1-111-1-1-1-1-1-11111-1-1-1-1-1-111-1-1-1-11111-1-111-1-1
χ1011111111111111-1-1-1-1111-1-1-1-11111111-1-1-1-111-1-1-1-11111111-11-1-1-111-1-11111-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-111-1-1-1-1-1-11111-1-111
χ1111111111111111-1-1-1-1111-1-1-1-11111111-1-1-1-111-1-1-1-1111111-11-1111-1-111-1-1-1-1111111-1-111-1-1-1-1-1-1-1-11111-1-111-1-11111-1-1-1-1-1-111
χ1211111111111111-1-1-1-1111-1-1-1-11111111-1-1-1-111-1-1-1-1111111-1-1-1-111-1-1-1-111-1-1-1-1111111-1-111111111-1-1-1-1-1-111-1-111-1-1-1-11111-1-1
χ1311111111111111-1-1-1-1111-1-1-1-11111111-1-1-1-111-1-1-1-111-1-1-1-11111-1-11111-1-11111-1-1-1-111-1-1-1-1-1-11111-1-1-1-111-1-11111-1-1-1-111-1-111
χ1411111111111111-1-1-1-1111-1-1-1-11111111-1-1-1-111-1-1-1-111-1-1-1-11-11-1-1-111-1-11111-1-1-1-1-1-1-1-1111111-1-1-1-1111111-1-1111111-1-1-1-111-1-1
χ1511111111111111-1-1-1-1111-1-1-1-11111111-1-1-1-111-1-1-1-111-1-1-1-1-11-1111-1-111-1-1-1-1111111-1-111-1-1-1-1-1-1-1-1111111-1-111-1-1-1-1111111-1-1
χ1611111111111111-1-1-1-1111-1-1-1-11111111-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-1111111-1-111111111-1-1-1-111-1-111-1-11111-1-1-1-111
χ17222222222222222222222-2-2-2-2-2-2-2-22222222-2-2-2-2-2-2-2-2222200000000000000000000000000000000000022-2-2-2-2000000000000
χ18222222222222222222222-2-2-2-2-2-2-2-22222222-2-2-2-2-2-2-2-2-2-2-2-2000000000000000000000000000000000000-2-22222000000000000
χ1922222222222222-2-2-2-22222222-2-2-2-2222-2-2-2-2-2-22222-2-22222000000000000000000000000000000000000-2-2-2-222000000000000
χ2022222222222222-2-2-2-22222222-2-2-2-2222-2-2-2-2-2-22222-2-2-2-2-2-20000000000000000000000000000000000002222-2-2000000000000
χ212222222-1222-1-1-12222-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000222222-1-1-1-122-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1000000000000000000
χ222222222-1222-1-1-12222-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-100002-22-222-1-111-2-2-1-111-1-1-1-1-2-2-2-2111111111111000000000000000000
χ232222222-1222-1-1-12222-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000-22-22-2-211-1-12211-1-11111-2-2-2-2-1-1-1-111111111000000000000000000
χ242222222-1222-1-1-12222-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000-2-2-2-2-2-21111-2-21111111122221111-1-1-1-1-1-1-1-1000000000000000000
χ252222222-1222-1-1-1-2-2-2-2-1-1-1-2-2-2-22222-1-1-11111-1-11111-1-100002222-2-2-1-1-1-1-2-2-1-1-1-1111122-2-21111-1-1-1-11111000000000000000000
χ262222222-1222-1-1-1-2-2-2-2-1-1-1-2-2-2-22222-1-1-11111-1-11111-1-100002-22-2-2-2-1-11122-1-1111111-2-222-1-1-1-11111-1-1-1-1000000000000000000
χ272222222-1222-1-1-1-2-2-2-2-1-1-1-2-2-2-22222-1-1-11111-1-11111-1-10000-22-222211-1-1-2-211-1-1-1-1-1-1-2-22211111111-1-1-1-1000000000000000000
χ282222222-1222-1-1-1-2-2-2-2-1-1-1-2-2-2-22222-1-1-11111-1-11111-1-10000-2-2-2-2221111221111-1-1-1-122-2-2-1-1-1-1-1-1-1-11111000000000000000000
χ2922222-2-22-22-22222i2i−2i−2i2-2-22i2i−2i−2i2-22-2-22-22i2i−2i−2i2-22i2i−2i−2i2-20000000000000000000000000000000000000000000000000000002i−2i2-2
χ3022222-2-22-22-22222i2i−2i−2i2-2-22i2i−2i−2i2-22-2-22-22i2i−2i−2i2-22i2i−2i−2i2-2000000000000000000000000000000000000000000000000000000−2i2i-22
χ3122222-2-22-22-22222i2i−2i−2i2-2-2−2i−2i2i2i-22-22-22-22i2i−2i−2i-22−2i−2i2i2i-220000000000000000000000002-22i−2i000022-2-22i2i−2i−2i000000000000000000
χ3222222-2-22-22-22222i2i−2i−2i2-2-2−2i−2i2i2i-22-22-22-22i2i−2i−2i-22−2i−2i2i2i-22000000000000000000000000-22−2i2i0000-2-222−2i−2i2i2i000000000000000000
χ3322222-2-22-22-2222−2i−2i2i2i2-2-22i2i−2i−2i-22-22-22-2−2i−2i2i2i-222i2i−2i−2i-220000000000000000000000002-2−2i2i000022-2-2−2i−2i2i2i000000000000000000
χ3422222-2-22-22-2222−2i−2i2i2i2-2-22i2i−2i−2i-22-22-22-2−2i−2i2i2i-222i2i−2i−2i-22000000000000000000000000-222i−2i0000-2-2222i2i−2i−2i000000000000000000
χ3522222-2-22-22-2222−2i−2i2i2i2-2-2−2i−2i2i2i2-22-2-22-2−2i−2i2i2i2-2−2i−2i2i2i2-20000000000000000000000000000000000000000000000000000002i−2i-22
χ3622222-2-22-22-2222−2i−2i2i2i2-2-2−2i−2i2i2i2-22-2-22-2−2i−2i2i2i2-2−2i−2i2i2i2-2000000000000000000000000000000000000000000000000000000−2i2i2-2
χ3722222-2-2-1-22-2-1-1-12i2i−2i−2i-111−2i−2i2i2i-22-221-11−i−iii1-1ii−i−i1-10000000000−i3i3−i3i300−i3i3−i3i333−3−32-22i−2i33−3−3-1-111−i−iii000000000000000000
χ3822222-2-2-1-22-2-1-1-12i2i−2i−2i-111−2i−2i2i2i-22-221-11−i−iii1-1ii−i−i1-10000000000−i3i3i3−i300−i3i3i3−i333−3−3-22−2i2i−3−33311-1-1ii−i−i000000000000000000
χ3922222-2-2-1-22-2-1-1-12i2i−2i−2i-111−2i−2i2i2i-22-221-11−i−iii1-1ii−i−i1-10000000000i3−i3−i3i300i3−i3−i3i3−3−333-22−2i2i33−3−311-1-1ii−i−i000000000000000000
χ4022222-2-2-1-22-2-1-1-12i2i−2i−2i-111−2i−2i2i2i-22-221-11−i−iii1-1ii−i−i1-10000000000i3−i3i3−i300i3−i3i3−i3−3−3332-22i−2i−3−333-1-111−i−iii000000000000000000
χ4122222-2-2-1-22-2-1-1-1−2i−2i2i2i-1112i2i−2i−2i-22-221-11ii−i−i1-1−i−iii1-10000000000−i3i3−i3i300−i3i3−i3i3−3−3332-2−2i2i−3−333-1-111ii−i−i000000000000000000
χ4222222-2-2-1-22-2-1-1-1−2i−2i2i2i-1112i2i−2i−2i-22-221-11ii−i−i1-1−i−iii1-10000000000−i3i3i3−i300−i3i3i3−i3−3−333-222i−2i33−3−311-1-1−i−iii000000000000000000
χ4322222-2-2-1-22-2-1-1-1−2i−2i2i2i-1112i2i−2i−2i-22-221-11ii−i−i1-1−i−iii1-10000000000i3−i3−i3i300i3−i3−i3i333−3−3-222i−2i−3−33311-1-1−i−iii000000000000000000
χ4422222-2-2-1-22-2-1-1-1−2i−2i2i2i-1112i2i−2i−2i-22-221-11ii−i−i1-1−i−iii1-10000000000i3−i3i3−i300i3−i3i3−i333−3−32-2−2i2i33−3−3-1-111ii−i−i000000000000000000
χ4522-2-2-22-2222-22-2-22i−2i2i−2i-22-22i−2i2i−2i2-2-2222-22i−2i2i−2i-222i−2i2i−2i2-20000000000000000000000000000000000000000000000002-2002i−2i0000
χ4622-2-2-22-2222-22-2-22i−2i2i−2i-22-22i−2i2i−2i2-2-2222-22i−2i2i−2i-222i−2i2i−2i2-2000000000000000000000000000000000000000000000000-2200−2i2i0000
χ4722-2-2-22-2222-22-2-22i−2i2i−2i-22-2−2i2i−2i2i-222-222-22i−2i2i−2i2-2−2i2i−2i2i-220000020-20000222i−2i00-2-2000000002i−2i2i−2i00000000000000000000000000
χ4822-2-2-22-2222-22-2-22i−2i2i−2i-22-2−2i2i−2i2i-222-222-22i−2i2i−2i2-2−2i2i−2i2i-2200000-2020000-2-2−2i2i002200000000−2i2i−2i2i00000000000000000000000000
χ4922-2-2-22-2222-22-2-2−2i2i−2i2i-22-22i−2i2i−2i-222-222-2−2i2i−2i2i2-22i−2i2i−2i-220000020-2000022−2i2i00-2-200000000−2i2i−2i2i00000000000000000000000000
χ5022-2-2-22-2222-22-2-2−2i2i−2i2i-22-22i−2i2i−2i-222-222-2−2i2i−2i2i2-22i−2i2i−2i-2200000-2020000-2-22i−2i0022000000002i−2i2i−2i00000000000000000000000000
χ5122-2-2-22-2222-22-2-2−2i2i−2i2i-22-2−2i2i−2i2i2-2-2222-2−2i2i−2i2i-22−2i2i−2i2i2-20000000000000000000000000000000000000000000000002-200−2i2i0000
χ5222-2-2-22-2222-22-2-2−2i2i−2i2i-22-2−2i2i−2i2i2-2-2222-2−2i2i−2i2i-22−2i2i−2i2i2-2000000000000000000000000000000000000000000000000-22002i−2i0000
χ5322-2-2-22-2-122-2-1112i−2i2i−2i1-11−2i2i−2i2i-222-2-1-11−ii−ii-11i−ii−i1-10000020-200−i3i3-1-12i−2ii3−i3113−33−30000−ii−ii−i3i3−i3i33−33−3000000000000000000
χ5422-2-2-22-2-122-2-1112i−2i2i−2i1-11−2i2i−2i2i-222-2-1-11−ii−ii-11i−ii−i1-10000020-200i3−i3-1-12i−2i−i3i311−33−330000−ii−iii3−i3i3−i3−33−33000000000000000000
χ5522-2-2-22-2-122-2-1112i−2i2i−2i1-11−2i2i−2i2i-222-2-1-11−ii−ii-11i−ii−i1-100000-20200−i3i311−2i2ii3−i3-1-13−33−30000i−ii−ii3−i3i3−i3−33−33000000000000000000
χ5622-2-2-22-2-122-2-1112i−2i2i−2i1-11−2i2i−2i2i-222-2-1-11−ii−ii-11i−ii−i1-100000-20200i3−i311−2i2i−i3i3-1-1−33−330000i−ii−i−i3i3−i3i33−33−3000000000000000000
χ5722-2-2-22-2-122-2-111−2i2i−2i2i1-112i−2i2i−2i-222-2-1-11i−ii−i-11−ii−ii1-10000020-200−i3i3-1-1−2i2ii3−i311−33−330000i−ii−i−i3i3−i3i3−33−33000000000000000000
χ5822-2-2-22-2-122-2-111−2i2i−2i2i1-112i−2i2i−2i-222-2-1-11i−ii−i-11−ii−ii1-10000020-200i3−i3-1-1−2i2i−i3i3113−33−30000i−ii−ii3−i3i3−i33−33−3000000000000000000
χ5922-2-2-22-2-122-2-111−2i2i−2i2i1-112i−2i2i−2i-222-2-1-11i−ii−i-11−ii−ii1-100000-20200−i3i3112i−2ii3−i3-1-1−33−330000−ii−iii3−i3i3−i33−33−3000000000000000000
χ6022-2-2-22-2-122-2-111−2i2i−2i2i1-112i−2i2i−2i-222-2-1-11i−ii−i-11−ii−ii1-100000-20200i3−i3112i−2i−i3i3-1-13−33−30000−ii−ii−i3i3−i3i3−33−33000000000000000000
χ6122-2-2-2-222-2222-2-22-2-22-2-222-2-2222-2-2-2222-2-22-2-22-2-2222000020-202-2220000-2-2002-2-220000000000000000000000000000000000
χ6222-2-2-2-222-2222-2-22-2-22-2-222-2-2222-2-2-2222-2-22-2-22-2-22220000-2020-22-2-200002200-222-20000000000000000000000000000000000
χ6322-2-2-2-222-2222-2-22-2-22-2-22-222-2-2-222-2222-2-2222-222-2-2-200000000000000000000000000000000000000000000002-2002-2000000
χ6422-2-2-2-222-2222-2-22-2-22-2-22-222-2-2-222-2222-2-2222-222-2-2-20000000000000000000000000000000000000000000000-2200-22000000
χ6522-2-2-2-222-2222-2-2-222-2-2-222-2-22-2-222-222-222-2222-2-22-2-200000000000000000000000000000000000000000000002-200-22000000
χ6622-2-2-2-222-2222-2-2-222-2-2-222-2-22-2-222-222-222-2222-2-22-2-20000000000000000000000000000000000000000000000-22002-2000000
χ6722-2-2-2-222-2222-2-2-222-2-2-22-222-222-2-2-222-222-2-2-2-222-222000020-20-22220000-2-200-222-20000000000000000000000000000000000
χ6822-2-2-2-222-2222-2-2-222-2-2-22-222-222-2-2-222-222-2-2-2-222-2220000-20202-2-2-2000022002-2-220000000000000000000000000000000000
χ6922-2-2-2-22-1-222-1112-2-2211-12-2-2222-2-21-1-1-111-111-111-1-1-1000020-202-2-1-1−i3i30011i3−i3-111-10000−i3i3i3−i3−i3i3i3−i3−i3i3i3−i3000000000000000000
χ7022-2-2-2-22-1-222-1112-2-2211-12-2-2222-2-21-1-1-111-111-111-1-1-1000020-202-2-1-1i3−i30011−i3i3-111-10000i3−i3−i3i3i3−i3−i3i3i3−i3−i3i3000000000000000000
χ7122-2-2-2-22-1-222-1112-2-2211-12-2-2222-2-21-1-1-111-111-111-1-1-10000-2020-2211−i3i300-1-1i3−i31-1-110000−i3i3i3−i3i3−i3−i3i3i3−i3−i3i3000000000000000000
χ7222-2-2-2-22-1-222-1112-2-2211-12-2-2222-2-21-1-1-111-111-111-1-1-10000-2020-2211i3−i300-1-1−i3i31-1-110000i3−i3−i3i3−i3i3i3−i3−i3i3i3−i3000000000000000000
χ7322-2-2-2-22-1-222-111-222-211-1-222-222-2-21-1-11-1-11111-1-11-1-1000020-20-22-1-1−i3i30011i3−i31-1-110000i3−i3−i3i3−i3i3i3−i3i3−i3−i3i3000000000000000000
χ7422-2-2-2-22-1-222-111-222-211-1-222-222-2-21-1-11-1-11111-1-11-1-1000020-20-22-1-1i3−i30011−i3i31-1-110000−i3i3i3−i3i3−i3−i3i3−i3i3i3−i3000000000000000000
χ7522-2-2-2-22-1-222-111-222-211-1-222-222-2-21-1-11-1-11111-1-11-1-10000-20202-211−i3i300-1-1i3−i3-111-10000i3−i3−i3i3i3−i3−i3i3−i3i3i3−i3000000000000000000
χ7622-2-2-2-22-1-222-111-222-211-1-222-222-2-21-1-11-1-11111-1-11-1-10000-20202-211i3−i300-1-1−i3i3-111-10000−i3i3i3−i3−i3i3i3−i3i3−i3−i3i3000000000000000000
χ774444444-2444-2-2-24444-2-2-2-4-4-4-4-4-4-4-4-2-2-2-2-2-2-2222222220000000000000000000000000000000000000000000000000000000000
χ784444444-2444-2-2-2-4-4-4-4-2-2-24444-4-4-4-4-2-2-2222222-2-2-2-2220000000000000000000000000000000000000000000000000000000000
χ7944444-4-4-2-44-4-2-2-24i4i−4i−4i-2224i4i−4i−4i4-44-42-22−2i−2i2i2i-22−2i−2i2i2i-220000000000000000000000000000000000000000000000000000000000
χ8044444-4-4-2-44-4-2-2-2−4i−4i4i4i-222−4i−4i4i4i4-44-42-222i2i−2i−2i-222i2i−2i−2i-220000000000000000000000000000000000000000000000000000000000
χ814444-44-44-4-444440000-44-400000000-4-44000000000000000000000000000000000000000000000000000000004-4000000000000
χ824444-44-44-4-444440000-44-400000000-4-4400000000000000000000000000000000000000000000000000000000-44000000000000
χ834444-4-4444-4-44440000-4-44000000004-4-400000000000000000000000000000000000000000000000000004-40000000000000000
χ844444-4-4444-4-44440000-4-44000000004-4-40000000000000000000000000000000000000000000000000000-440000000000000000
χ8544-4-44444-4-4-44-4-4000044400000000-4-4-400000000000044-4-4000000000000000000000000000000000000000000000000000000
χ8644-4-44444-4-4-44-4-4000044400000000-4-4-4000000000000-4-444000000000000000000000000000000000000000000000000000000
χ8744-4-44-4-444-444-4-400004-4-4000000004-440000000000000000000000000000000000000000000000000000004i−4i00000000000000
χ8844-4-44-4-444-444-4-400004-4-4000000004-44000000000000000000000000000000000000000000000000000000−4i4i00000000000000
χ8944-4-4-44-4-244-4-2224i−4i4i−4i2-224i−4i4i−4i4-4-44-2-22−2i2i−2i2i2-2−2i2i−2i2i-220000000000000000000000000000000000000000000000000000000000
χ9044-4-4-44-4-244-4-222−4i4i−4i4i2-22−4i4i−4i4i4-4-44-2-222i−2i2i−2i2-22i−2i2i−2i-220000000000000000000000000000000000000000000000000000000000
χ9144-4-4-4-44-2-444-2224-4-4422-2-444-4-4-4442-2-2-222-2-2-22-2-22220000000000000000000000000000000000000000000000000000000000
χ9244-4-4-4-44-2-444-222-444-422-24-4-44-4-4442-2-22-2-22-2-2-222-2220000000000000000000000000000000000000000000000000000000000
χ938888-88-8-4-8-88-4-4-400004-440000000044-40000000000000000000000000000000000000000000000000000000000000000000000
χ948888-8-88-48-8-8-4-4-4000044-400000000-4440000000000000000000000000000000000000000000000000000000000000000000000
χ9588-8-8888-4-8-8-8-4440000-4-4-4000000004440000000000000000000000000000000000000000000000000000000000000000000000
χ9688-8-88-8-8-48-88-4440000-44400000000-44-40000000000000000000000000000000000000000000000000000000000000000000000
χ978-88i−8i0008000-88i−8i0000000000000000000000000000004-44i−4i000000000000000000000000000000000000000000000000000000
χ988-88i−8i0008000-88i−8i000000000000000000000000000000-44−4i4i000000000000000000000000000000000000000000000000000000
χ998-8−8i8i0008000-8−8i8i0000000000000000000000000000004-4−4i4i000000000000000000000000000000000000000000000000000000
χ1008-8−8i8i0008000-8−8i8i000000000000000000000000000000-444i−4i000000000000000000000000000000000000000000000000000000
χ10116-1616i−16i000-80008−8i8i0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ10216-16−16i16i000-800088i−8i0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000

Here i is the imaginary unit (i² = −1).