Finite Group Databasebeta

← Group #10823595

Character table — Group #10823595

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96
size11111111222222222222222222224444444444448888888888888888888888888888888888881212121212121212242424242424242424242424
order122222223444444444444666666612121212121212121212121244444444888812121212121212121212121212121212242424242424242488888888244444444444
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111-1-111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-11111-1-1-1-1-1-1-1
χ4111111111111111111111111111111111111111111-1-111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-11111111
χ51111111111111111111111111111111111111111-1-111-1-111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-111-111-1
χ61111111111111111111111111111111111111111-1-111-1-111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-11-1-11
χ71111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111111-1-1-1-11-1-11-1-11
χ81111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-11111-111-111-1
χ9111111111-1-1-1-1-1-1-1-111111111111-1-1-1-1-1-1-1-111111111-1-1-1-111-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1111-1-1-1-1-1-1111
χ10111111111-1-1-1-1-1-1-1-111111111111-1-1-1-1-1-1-1-111111111-1-1-1-111-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1111111-1-1-1
χ11111111111-1-1-1-1-1-1-1-111111111111-1-1-1-1-1-1-1-1111111-1-1-1-111-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-111-1-11111-1-1-1
χ12111111111-1-1-1-1-1-1-1-111111111111-1-1-1-1-1-1-1-1111111-1-1-1-111-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-111111-1-111-1-1-1-1111
χ13111111111-1-1-1-1-1-1-1-111111111111-1-1-1-1-1-1-1-11111-1-11111-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1111-1-1111-1
χ14111111111-1-1-1-1-1-1-1-111111111111-1-1-1-1-1-1-1-11111-1-11111-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-11111111-1-1-111-1-1-11
χ15111111111-1-1-1-1-1-1-1-111111111111-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-11111-1-1-1-11-1-111-111-1-1-11
χ16111111111-1-1-1-1-1-1-1-111111111111-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-11111-111-1-11-1-1111-1
χ172222222222222-2-2-2-2-2-2-2-222222222222-2-2-2-2-2-2-2-20000000000000000000000000000000000000000000020000-200200-2
χ182222222222222-2-2-2-2-2-2-2-222222222222-2-2-2-2-2-2-2-200000000000000000000000000000000000000000000-20000200-2002
χ19222222222-2-2-2-22222-2-2-2-22222222-2-2-2-22222-2-2-2-20000000000000000000000000000000000000000000020000200-200-2
χ20222222222-2-2-2-22222-2-2-2-22222222-2-2-2-22222-2-2-2-200000000000000000000000000000000000000000000-20000-2002002
χ2122222222-1222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-100000000000000000000
χ2222222222-1222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122-2-222-2-2-2-2-2-2-1-1-1-11111-1-1-1-111111111111100000000000000000000
χ2322222222-1222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-222-2-222-2-2-2-21111-1-1-1-11111-1-1-1-11111111100000000000000000000
χ2422222222-1222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-222221111111111111111-1-1-1-1-1-1-1-100000000000000000000
χ2522222222-1-2-2-2-2-2-2-2-22222-1-1-1-1-1-1-111111111-1-1-1-12222-2-2-2-222-2-2-1-1-1-1-1-1-1-111111111-1-1-1-1111100000000000000000000
χ2622222222-1-2-2-2-2-2-2-2-22222-1-1-1-1-1-1-111111111-1-1-1-122-2-2-2-222-2-222-1-1-1-111111111-1-1-1-11111-1-1-1-100000000000000000000
χ2722222222-1-2-2-2-2-2-2-2-22222-1-1-1-1-1-1-111111111-1-1-1-1-2-22222-2-2-2-2221111-1-1-1-1-1-1-1-111111111-1-1-1-100000000000000000000
χ2822222222-1-2-2-2-2-2-2-2-22222-1-1-1-1-1-1-111111111-1-1-1-1-2-2-2-2222222-2-211111111-1-1-1-1-1-1-1-1-1-1-1-1111100000000000000000000
χ2922-22-2-2-2222i2i−2i−2i2i2i−2i−2i2-22-222-2-2-2-222i2i−2i−2i2i2i−2i−2i2-22-20000000000000000000000000000000000000000000002i−2i2-20000000
χ3022-22-2-2-2222i2i−2i−2i2i2i−2i−2i2-22-222-2-2-2-222i2i−2i−2i2i2i−2i−2i2-22-2000000000000000000000000000000000000000000000−2i2i-220000000
χ3122-22-2-2-2222i2i−2i−2i−2i−2i2i2i-22-2222-2-2-2-222i2i−2i−2i−2i−2i2i2i-22-22002i−2i002-2000000002i2i−2i−2i000022-2-20000000000000000000000000000
χ3222-22-2-2-2222i2i−2i−2i−2i−2i2i2i-22-2222-2-2-2-222i2i−2i−2i−2i−2i2i2i-22-2200−2i2i00-2200000000−2i−2i2i2i0000-2-2220000000000000000000000000000
χ3322-22-2-2-222−2i−2i2i2i2i2i−2i−2i-22-2222-2-2-2-22−2i−2i2i2i2i2i−2i−2i-22-22002i−2i00-22000000002i2i−2i−2i0000-2-2220000000000000000000000000000
χ3422-22-2-2-222−2i−2i2i2i2i2i−2i−2i-22-2222-2-2-2-22−2i−2i2i2i2i2i−2i−2i-22-2200−2i2i002-200000000−2i−2i2i2i000022-2-20000000000000000000000000000
χ3522-22-2-2-222−2i−2i2i2i−2i−2i2i2i2-22-222-2-2-2-22−2i−2i2i2i−2i−2i2i2i2-22-20000000000000000000000000000000000000000000002i−2i-220000000
χ3622-22-2-2-222−2i−2i2i2i−2i−2i2i2i2-22-222-2-2-2-22−2i−2i2i2i−2i−2i2i2i2-22-2000000000000000000000000000000000000000000000−2i2i2-20000000
χ3722-22-2-2-22-12i2i−2i−2i−2i−2i2i2i-22-22-1-11111-1−i−iiiii−i−i1-11-1002i−2i002-2000033−3−3−i−iii−i3−i3i3i3-1-111−i3−i3i3i333−3−300000000000000000000
χ3822-22-2-2-22-12i2i−2i−2i−2i−2i2i2i-22-22-1-11111-1−i−iiiii−i−i1-11-1002i−2i002-20000−3−333−i−iiii3i3−i3−i3-1-111i3i3−i3−i3−3−33300000000000000000000
χ3922-22-2-2-22-12i2i−2i−2i−2i−2i2i2i-22-22-1-11111-1−i−iiiii−i−i1-11-100−2i2i00-22000033−3−3ii−i−i−i3−i3i3i311-1-1i3i3−i3−i3−3−33300000000000000000000
χ4022-22-2-2-22-12i2i−2i−2i−2i−2i2i2i-22-22-1-11111-1−i−iiiii−i−i1-11-100−2i2i00-220000−3−333ii−i−ii3i3−i3−i311-1-1−i3−i3i3i333−3−300000000000000000000
χ4122-22-2-2-22-1−2i−2i2i2i2i2i−2i−2i-22-22-1-11111-1ii−i−i−i−iii1-11-1002i−2i00-22000033−3−3−i−iiii3i3−i3−i311-1-1−i3−i3i3i3−3−33300000000000000000000
χ4222-22-2-2-22-1−2i−2i2i2i2i2i−2i−2i-22-22-1-11111-1ii−i−i−i−iii1-11-1002i−2i00-220000−3−333−i−iii−i3−i3i3i311-1-1i3i3−i3−i333−3−300000000000000000000
χ4322-22-2-2-22-1−2i−2i2i2i2i2i−2i−2i-22-22-1-11111-1ii−i−i−i−iii1-11-100−2i2i002-2000033−3−3ii−i−ii3i3−i3−i3-1-111i3i3−i3−i333−3−300000000000000000000
χ4422-22-2-2-22-1−2i−2i2i2i2i2i−2i−2i-22-22-1-11111-1ii−i−i−i−iii1-11-100−2i2i002-20000−3−333ii−i−i−i3−i3i3i3-1-111−i3−i3i3i3−3−33300000000000000000000
χ452-22-22-2-2222i−2i2i−2i2i−2i2i−2i2-2-22-2-222-2-222i−2i2i−2i2i−2i2i−2i-222-20000000000000000000000000000000000002i2i−2i−2i22-2-2000000000000
χ462-22-22-2-2222i−2i2i−2i2i−2i2i−2i2-2-22-2-222-2-222i−2i2i−2i2i−2i2i−2i-222-2000000000000000000000000000000000000−2i−2i2i2i-2-222000000000000
χ472-22-22-2-2222i−2i2i−2i−2i2i−2i2i-222-2-2-222-2-222i−2i2i−2i−2i2i−2i2i2-2-22000000002-22i−2i00000000000000002-22-22i−2i2i−2i00000000000000000000
χ482-22-22-2-2222i−2i2i−2i−2i2i−2i2i-222-2-2-222-2-222i−2i2i−2i−2i2i−2i2i2-2-2200000000-22−2i2i0000000000000000-22-22−2i2i−2i2i00000000000000000000
χ492-22-22-2-222−2i2i−2i2i2i−2i2i−2i-222-2-2-222-2-22−2i2i−2i2i2i−2i2i−2i2-2-22000000002-2−2i2i00000000000000002-22-2−2i2i−2i2i00000000000000000000
χ502-22-22-2-222−2i2i−2i2i2i−2i2i−2i-222-2-2-222-2-22−2i2i−2i2i2i−2i2i−2i2-2-2200000000-222i−2i0000000000000000-22-222i−2i2i−2i00000000000000000000
χ512-22-22-2-222−2i2i−2i2i−2i2i−2i2i2-2-22-2-222-2-22−2i2i−2i2i−2i2i−2i2i-222-20000000000000000000000000000000000002i2i−2i−2i-2-222000000000000
χ522-22-22-2-222−2i2i−2i2i−2i2i−2i2i2-2-22-2-222-2-22−2i2i−2i2i−2i2i−2i2i-222-2000000000000000000000000000000000000−2i−2i2i2i22-2-2000000000000
χ532-22-22-2-22-12i−2i2i−2i−2i2i−2i2i-222-211-1-111-1−ii−iii−ii−i-111-1000000002-22i−2i3−33−33−33−3−i3i3−i3i3−i3i3−i3i3-11-11−ii−ii00000000000000000000
χ542-22-22-2-22-12i−2i2i−2i−2i2i−2i2i-222-211-1-111-1−ii−iii−ii−i-111-1000000002-22i−2i−33−33−33−33i3−i3i3−i3i3−i3i3−i3-11-11−ii−ii00000000000000000000
χ552-22-22-2-22-12i−2i2i−2i−2i2i−2i2i-222-211-1-111-1−ii−iii−ii−i-111-100000000-22−2i2i3−33−3−33−33−i3i3−i3i3i3−i3i3−i31-11-1i−ii−i00000000000000000000
χ562-22-22-2-22-12i−2i2i−2i−2i2i−2i2i-222-211-1-111-1−ii−iii−ii−i-111-100000000-22−2i2i−33−333−33−3i3−i3i3−i3−i3i3−i3i31-11-1i−ii−i00000000000000000000
χ572-22-22-2-22-1−2i2i−2i2i2i−2i2i−2i-222-211-1-111-1i−ii−i−ii−ii-111-1000000002-2−2i2i3−33−33−33−3i3−i3i3−i3i3−i3i3−i3-11-11i−ii−i00000000000000000000
χ582-22-22-2-22-1−2i2i−2i2i2i−2i2i−2i-222-211-1-111-1i−ii−i−ii−ii-111-1000000002-2−2i2i−33−33−33−33−i3i3−i3i3−i3i3−i3i3-11-11i−ii−i00000000000000000000
χ592-22-22-2-22-1−2i2i−2i2i2i−2i2i−2i-222-211-1-111-1i−ii−i−ii−ii-111-100000000-222i−2i3−33−3−33−33i3−i3i3−i3−i3i3−i3i31-11-1−ii−ii00000000000000000000
χ602-22-22-2-22-1−2i2i−2i2i2i−2i2i−2i-222-211-1-111-1i−ii−i−ii−ii-111-100000000-222i−2i−33−333−33−3−i3i3−i3i3i3−i3i3−i31-11-1−ii−ii00000000000000000000
χ612-2-2-2-222222-2-222-2-2222-2-2-2-2-2-22222-2-222-2-22-2-2222-2002-20000002-2-2200002-2-2200000000000000000000000000000000
χ622-2-2-2-222222-2-222-2-2222-2-2-2-2-2-22222-2-222-2-22-2-222-2200-22000000-222-20000-222-200000000000000000000000000000000
χ632-2-2-2-222222-2-22-222-2-2-222-2-2-2-22222-2-22-222-222-2-2000000000000000000000000000000000000000000000000002-202-20
χ642-2-2-2-222222-2-22-222-2-2-222-2-2-2-22222-2-22-222-222-2-200000000000000000000000000000000000000000000000000-220-220
χ652-2-2-2-22222-222-22-2-22-2-222-2-2-2-2222-222-22-2-2222-2-2000000000000000000000000000000000000000000000000002-20-220
χ662-2-2-2-22222-222-22-2-22-2-222-2-2-2-2222-222-22-2-2222-2-200000000000000000000000000000000000000000000000000-2202-20
χ672-2-2-2-22222-222-2-222-222-2-2-2-2-2-2222-222-2-222-2-2-2222-200-220000002-2-220000-222-200000000000000000000000000000000
χ682-2-2-2-22222-222-2-222-222-2-2-2-2-2-2222-222-2-222-2-2-222-22002-2000000-222-200002-2-2200000000000000000000000000000000
χ692-2-2-2-2222-12-2-222-2-2222-2-21111-1-1-1-111-1-111-111-1-12-2002-2000000-111-1−i3i3i3−i3-111-1−i3i3i3−i3−i3i3i3−i3−i3i3i3−i300000000000000000000
χ702-2-2-2-2222-12-2-222-2-2222-2-21111-1-1-1-111-1-111-111-1-12-2002-2000000-111-1i3−i3−i3i3-111-1i3−i3−i3i3i3−i3−i3i3i3−i3−i3i300000000000000000000
χ712-2-2-2-2222-12-2-222-2-2222-2-21111-1-1-1-111-1-111-111-1-1-2200-220000001-1-11−i3i3i3−i31-1-11−i3i3i3−i3i3−i3−i3i3i3−i3−i3i300000000000000000000
χ722-2-2-2-2222-12-2-222-2-2222-2-21111-1-1-1-111-1-111-111-1-1-2200-220000001-1-11i3−i3−i3i31-1-11i3−i3−i3i3−i3i3i3−i3−i3i3i3−i300000000000000000000
χ732-2-2-2-2222-1-222-2-222-222-2-21111-1-1-11-1-111-1-1111-1-12-200-22000000-111-1−i3i3i3−i31-1-11i3−i3−i3i3−i3i3i3−i3i3−i3−i3i300000000000000000000
χ742-2-2-2-2222-1-222-2-222-222-2-21111-1-1-11-1-111-1-1111-1-12-200-22000000-111-1i3−i3−i3i31-1-11−i3i3i3−i3i3−i3−i3i3−i3i3i3−i300000000000000000000
χ752-2-2-2-2222-1-222-2-222-222-2-21111-1-1-11-1-111-1-1111-1-1-22002-20000001-1-11−i3i3i3−i3-111-1i3−i3−i3i3i3−i3−i3i3−i3i3i3−i300000000000000000000
χ762-2-2-2-2222-1-222-2-222-222-2-21111-1-1-11-1-111-1-1111-1-1-22002-20000001-1-11i3−i3−i3i3-111-1−i3i3i3−i3−i3i3i3−i3i3−i3−i3i300000000000000000000
χ7744444444-24444-4-4-4-4-4-4-4-4-2-2-2-2-2-2-2-2-2-2-22222222200000000000000000000000000000000000000000000000000000000
χ7844444444-2-4-4-4-44444-4-4-4-4-2-2-2-2-2-2-22222-2-2-2-2222200000000000000000000000000000000000000000000000000000000
χ79444-4-4-44-440000000000004-44-44-4-4000000000000000000000000000000000000000000000000000022−2222−22000000000000
χ80444-4-4-44-440000000000004-44-44-4-40000000000000000000000000000000000000000000000000000−2222−2222000000000000
χ8144-44-4-4-44-24i4i−4i−4i4i4i−4i−4i4-44-4-2-22222-2−2i−2i2i2i−2i−2i2i2i-22-2200000000000000000000000000000000000000000000000000000000
χ8244-44-4-4-44-2−4i−4i4i4i−4i−4i4i4i4-44-4-2-22222-22i2i−2i−2i2i2i−2i−2i-22-2200000000000000000000000000000000000000000000000000000000
χ8344-4-444-4-440000000000004-4-44-44-400000000000000000000000000000000000000000000000022−2222−220000000000000000
χ8444-4-444-4-440000000000004-4-44-44-4000000000000000000000000000000000000000000000000−2222−22220000000000000000
χ854-444-44-4-44000000000000-444-4-44-4000000000000000000000000000000000000000000000000000022−22−2222000000000000
χ864-444-44-4-44000000000000-444-4-44-40000000000000000000000000000000000000000000000000000−222222−22000000000000
χ874-44-44-4-44-24i−4i4i−4i4i−4i4i−4i4-4-4422-2-222-2−2i2i−2i2i−2i2i−2i2i2-2-2200000000000000000000000000000000000000000000000000000000
χ884-44-44-4-44-2−4i4i−4i4i−4i4i−4i4i4-4-4422-2-222-22i−2i2i−2i2i−2i2i−2i2-2-2200000000000000000000000000000000000000000000000000000000
χ894-4-444-44-44000000000000-44-444-4-4000000000000000000000000000000000000000000000000−2i22i22i2−2i20000000000000000
χ904-4-444-44-44000000000000-44-444-4-40000000000000000000000000000000000000000000000002i2−2i2−2i22i20000000000000000
χ914-4-4-4-4444-24-4-44-444-4-4-4442222-2-2-2-222-22-2-22-2-22200000000000000000000000000000000000000000000000000000000
χ924-4-4-4-4444-2-444-44-4-44-4-4442222-2-2-22-2-22-222-2-2-22200000000000000000000000000000000000000000000000000000000
χ93888-8-8-88-8-4000000000000-44-44-44400000000000000000000000000000000000000000000000000000000000000000000
χ9488-8-888-8-8-4000000000000-444-44-4400000000000000000000000000000000000000000000000000000000000000000000
χ958-888-88-8-8-40000000000004-4-444-4400000000000000000000000000000000000000000000000000000000000000000000
χ968-8-888-88-8-40000000000004-44-4-44400000000000000000000000000000000000000000000000000000000000000000000

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