Finite Group Databasebeta

← Group #10825706

Character table — Group #10825706

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96
size11111111222222222222222222224444444444448888888888888888888888888888888888881212121212121212242424242424242424242424
order122222223444444444444666666612121212121212121212121244444444888812121212121212121212121212121212242424242424242488888888444444444444
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-111-111-1
χ411111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-11-1-11
χ51111111111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-111111111-11111-1-1-1-1-1-1-1
χ61111111111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-11111111
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
χ9111111111-1-1-1-111-1-1-1-111111111111-1-1-1-1-1-1-1-11111-1-111-1-111-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1111-1-1-1-1-1-1111
χ10111111111-1-1-1-111-1-1-1-111111111111-1-1-1-1-1-1-1-11111-1-111-1-111-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1111111-1-1-1
χ11111111111-1-1-1-111-1-1-1-111111111111-1-1-1-1-1-1-1-11111-1-1-1-111-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1111-1-1111-1
χ12111111111-1-1-1-111-1-1-1-111111111111-1-1-1-1-1-1-1-11111-1-1-1-111-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111111-1-1-111-1-1-11
χ13111111111-1-1-1-111-1-1-1-111111111111-1-1-1-1-1-1-1-111-1-11111-1-1-1-111-1-1-1-1-1-1-1-111111111-1-1-1-111111111-1-1-1-1-111-1-11111-1-1-1
χ14111111111-1-1-1-111-1-1-1-111111111111-1-1-1-1-1-1-1-111-1-11111-1-1-1-111-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-111111-1-111-1-1-1-1111
χ15111111111-1-1-1-111-1-1-1-111111111111-1-1-1-1-1-1-1-111-1-111-1-11111-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-11111-1-1-1-11-1-111-111-1-1-11
χ16111111111-1-1-1-111-1-1-1-111111111111-1-1-1-1-1-1-1-111-1-111-1-11111-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-11111-111-1-11-1-1111-1
χ172222222222222-2-2-2-2-2-2-2-22222222-2-22222-2-2-2-2-2-20000000000000000000000000000000000000000000020000200-200-2
χ182222222222222-2-2-2-2-2-2-2-22222222-2-22222-2-2-2-2-2-200000000000000000000000000000000000000000000-20000-2002002
χ19222222222-2-2-2-2-2-22222-2-22222222-2-2-2-2-2-22222-2-20000000000000000000000000000000000000000000020000-200200-2
χ20222222222-2-2-2-2-2-22222-2-22222222-2-2-2-2-2-22222-2-200000000000000000000000000000000000000000000-20000200-2002
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
χ2222222222-1222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12222-2-2-2-2-2-2-2-2-1-1-1-11111-1-1-1-111111111111100000000000000000000
χ2322222222-1222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-22222-2-2-2-21111-1-1-1-11111-1-1-1-11111111100000000000000000000
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
χ2522222222-1-2-2-2-222-2-2-2-222-1-1-1-1-1-1-1-1-111111111-1-122-2-222-2-222-2-2-1-1-1-111111111-1-1-1-1-1-1-1-1111100000000000000000000
χ2622222222-1-2-2-2-222-2-2-2-222-1-1-1-1-1-1-1-1-111111111-1-122-2-2-2-222-2-222-1-1-1-1-1-1-1-1111111111111-1-1-1-100000000000000000000
χ2722222222-1-2-2-2-222-2-2-2-222-1-1-1-1-1-1-1-1-111111111-1-1-2-22222-2-2-2-22211111111-1-1-1-1-1-1-1-11111-1-1-1-100000000000000000000
χ2822222222-1-2-2-2-222-2-2-2-222-1-1-1-1-1-1-1-1-111111111-1-1-2-222-2-22222-2-21111-1-1-1-1-1-1-1-11111-1-1-1-1111100000000000000000000
χ2922-222-2-2-2222-2-22222-2-2-2-2-2222-2-2-22222-2-222-2-2-2-20000000000000000000000000000000000000000000002-22-20000000
χ3022-222-2-2-2222-2-22222-2-2-2-2-2222-2-2-22222-2-222-2-2-2-2000000000000000000000000000000000000000000000-22-220000000
χ3122-222-2-2-2222-2-2-2-2-2-22222-2222-2-2-2-2-222-2-2-2-222222i−2i2i−2i000000002i2i−2i−2i00002i2i−2i−2i00000000000000000000000000000000
χ3222-222-2-2-2222-2-2-2-2-2-22222-2222-2-2-2-2-222-2-2-2-22222−2i2i−2i2i00000000−2i−2i2i2i0000−2i−2i2i2i00000000000000000000000000000000
χ3322-222-2-2-22-2-22222-2-222-2-2-2222-2-2-222-2-222-2-222-2-20000000000000000000000000000000000000000000002-2-220000000
χ3422-222-2-2-22-2-22222-2-222-2-2-2222-2-2-222-2-222-2-222-2-2000000000000000000000000000000000000000000000-222-20000000
χ3522-222-2-2-22-2-222-2-222-2-222-2222-2-2-2-2-2-2-22222-2-2222i−2i−2i2i000000002i2i−2i−2i0000−2i−2i2i2i00000000000000000000000000000000
χ3622-222-2-2-22-2-222-2-222-2-222-2222-2-2-2-2-2-2-22222-2-222−2i2i2i−2i00000000−2i−2i2i2i00002i2i−2i−2i00000000000000000000000000000000
χ3722-222-2-2-2-122-2-2-2-2-2-222221-1-1-111111-1-11111-1-1-1-12i−2i2i−2i00000000−i−iii33−3−3−i−iii33−3−3−i3−i3i3i3−i3−i3i3i300000000000000000000
χ3822-222-2-2-2-122-2-2-2-2-2-222221-1-1-111111-1-11111-1-1-1-12i−2i2i−2i00000000−i−iii−3−333−i−iii−3−333i3i3−i3−i3i3i3−i3−i300000000000000000000
χ3922-222-2-2-2-122-2-2-2-2-2-222221-1-1-111111-1-11111-1-1-1-1−2i2i−2i2i00000000ii−i−i33−3−3ii−i−i33−3−3i3i3−i3−i3i3i3−i3−i300000000000000000000
χ4022-222-2-2-2-122-2-2-2-2-2-222221-1-1-111111-1-11111-1-1-1-1−2i2i−2i2i00000000ii−i−i−3−333ii−i−i−3−333−i3−i3i3i3−i3−i3i3i300000000000000000000
χ4122-222-2-2-2-1-2-222-2-222-2-2221-1-1-11111111-1-1-1-111-1-12i−2i−2i2i00000000−i−iii33−3−3ii−i−i−3−333i3i3−i3−i3−i3−i3i3i300000000000000000000
χ4222-222-2-2-2-1-2-222-2-222-2-2221-1-1-11111111-1-1-1-111-1-12i−2i−2i2i00000000−i−iii−3−333ii−i−i33−3−3−i3−i3i3i3i3i3−i3−i300000000000000000000
χ4322-222-2-2-2-1-2-222-2-222-2-2221-1-1-11111111-1-1-1-111-1-1−2i2i2i−2i00000000ii−i−i33−3−3−i−iii−3−333−i3−i3i3i3i3i3−i3−i300000000000000000000
χ4422-222-2-2-2-1-2-222-2-222-2-2221-1-1-11111111-1-1-1-111-1-1−2i2i2i−2i00000000ii−i−i−3−333−i−iii33−3−3i3i3−i3−i3−i3−i3i3i300000000000000000000
χ452-222-2-2-2222i−2i2i−2i2-22i−2i2i−2i2-2-22-2-222-22-22i−2i2i−2i2i−2i2i−2i2-200000000000000000000000000000000000022-2-22i2i−2i−2i000000000000
χ462-222-2-2-2222i−2i2i−2i2-22i−2i2i−2i2-2-22-2-222-22-22i−2i2i−2i2i−2i2i−2i2-2000000000000000000000000000000000000-2-222−2i−2i2i2i000000000000
χ472-222-2-2-2222i−2i2i−2i-22−2i2i−2i2i-22-22-2-222-2-222i−2i2i−2i−2i2i−2i2i-22000000002i−2i2-200000000000000002i−2i2i−2i2-22-200000000000000000000
χ482-222-2-2-2222i−2i2i−2i-22−2i2i−2i2i-22-22-2-222-2-222i−2i2i−2i−2i2i−2i2i-2200000000−2i2i-220000000000000000−2i2i−2i2i-22-2200000000000000000000
χ492-222-2-2-222−2i2i−2i2i2-2−2i2i−2i2i2-2-22-2-222-22-2−2i2i−2i2i−2i2i−2i2i2-200000000000000000000000000000000000022-2-2−2i−2i2i2i000000000000
χ502-222-2-2-222−2i2i−2i2i2-2−2i2i−2i2i2-2-22-2-222-22-2−2i2i−2i2i−2i2i−2i2i2-2000000000000000000000000000000000000-2-2222i2i−2i−2i000000000000
χ512-222-2-2-222−2i2i−2i2i-222i−2i2i−2i-22-22-2-222-2-22−2i2i−2i2i2i−2i2i−2i-22000000002i−2i-2200000000000000002i−2i2i−2i-22-2200000000000000000000
χ522-222-2-2-222−2i2i−2i2i-222i−2i2i−2i-22-22-2-222-2-22−2i2i−2i2i2i−2i2i−2i-2200000000−2i2i2-20000000000000000−2i2i−2i2i2-22-200000000000000000000
χ532-222-2-2-22-12i−2i2i−2i-22−2i2i−2i2i-221-111-1-111-1−ii−iii−ii−i1-1000000002i−2i2-2−i3i3−i3i3−i3i3−i3i33−33−33−33−3−ii−ii-11-1100000000000000000000
χ542-222-2-2-22-12i−2i2i−2i-22−2i2i−2i2i-221-111-1-111-1−ii−iii−ii−i1-1000000002i−2i2-2i3−i3i3−i3i3−i3i3−i3−33−33−33−33−ii−ii-11-1100000000000000000000
χ552-222-2-2-22-12i−2i2i−2i-22−2i2i−2i2i-221-111-1-111-1−ii−iii−ii−i1-100000000−2i2i-22−i3i3−i3i3i3−i3i3−i33−33−3−33−33i−ii−i1-11-100000000000000000000
χ562-222-2-2-22-12i−2i2i−2i-22−2i2i−2i2i-221-111-1-111-1−ii−iii−ii−i1-100000000−2i2i-22i3−i3i3−i3−i3i3−i3i3−33−333−33−3i−ii−i1-11-100000000000000000000
χ572-222-2-2-22-1−2i2i−2i2i-222i−2i2i−2i-221-111-1-111-1i−ii−i−ii−ii1-1000000002i−2i-22−i3i3−i3i3i3−i3i3−i3−33−333−33−3−ii−ii1-11-100000000000000000000
χ582-222-2-2-22-1−2i2i−2i2i-222i−2i2i−2i-221-111-1-111-1i−ii−i−ii−ii1-1000000002i−2i-22i3−i3i3−i3−i3i3−i3i33−33−3−33−33−ii−ii1-11-100000000000000000000
χ592-222-2-2-22-1−2i2i−2i2i-222i−2i2i−2i-221-111-1-111-1i−ii−i−ii−ii1-100000000−2i2i2-2−i3i3−i3i3−i3i3−i3i3−33−33−33−33i−ii−i-11-1100000000000000000000
χ602-222-2-2-22-1−2i2i−2i2i-222i−2i2i−2i-221-111-1-111-1i−ii−i−ii−ii1-100000000−2i2i2-2i3−i3i3−i3i3−i3i3−i33−33−33−33−3i−ii−i-11-1100000000000000000000
χ612-2-22-222-222i−2i−2i2i2-22i−2i−2i2i-2222-2-2-2-222-22i−2i−2i2i2i−2i−2i2i-2200002-22i−2i000000002i−2i−2i2i0000-222-20000000000000000000000000000
χ622-2-22-222-222i−2i−2i2i2-22i−2i−2i2i-2222-2-2-2-222-22i−2i−2i2i2i−2i−2i2i-220000-22−2i2i00000000−2i2i2i−2i00002-2-220000000000000000000000000000
χ632-2-22-222-222i−2i−2i2i-22−2i2i2i−2i2-222-2-2-2-22-222i−2i−2i2i−2i2i2i−2i2-2000000000000000000000000000000000000000000000000002-202i−2i0
χ642-2-22-222-222i−2i−2i2i-22−2i2i2i−2i2-222-2-2-2-22-222i−2i−2i2i−2i2i2i−2i2-200000000000000000000000000000000000000000000000000-220−2i2i0
χ652-2-22-222-22−2i2i2i−2i2-2−2i2i2i−2i-2222-2-2-2-222-2−2i2i2i−2i−2i2i2i−2i-2200002-2−2i2i00000000−2i2i2i−2i0000-222-20000000000000000000000000000
χ662-2-22-222-22−2i2i2i−2i2-2−2i2i2i−2i-2222-2-2-2-222-2−2i2i2i−2i−2i2i2i−2i-220000-222i−2i000000002i−2i−2i2i00002-2-220000000000000000000000000000
χ672-2-22-222-22−2i2i2i−2i-222i−2i−2i2i2-222-2-2-2-22-22−2i2i2i−2i2i−2i−2i2i2-2000000000000000000000000000000000000000000000000002-20−2i2i0
χ682-2-22-222-22−2i2i2i−2i-222i−2i−2i2i2-222-2-2-2-22-22−2i2i2i−2i2i−2i−2i2i2-200000000000000000000000000000000000000000000000000-2202i−2i0
χ692-2-22-222-2-12i−2i−2i2i2-22i−2i−2i2i-22-1-11111-1-11−iii−i−iii−i1-100002-22i−2i00003−3−33−iii−ii3−i3−i3i31-1-113−3−33−i3i3i3−i300000000000000000000
χ702-2-22-222-2-12i−2i−2i2i2-22i−2i−2i2i-22-1-11111-1-11−iii−i−iii−i1-100002-22i−2i0000−333−3−iii−i−i3i3i3−i31-1-11−333−3i3−i3−i3i300000000000000000000
χ712-2-22-222-2-12i−2i−2i2i2-22i−2i−2i2i-22-1-11111-1-11−iii−i−iii−i1-10000-22−2i2i00003−3−33i−i−iii3−i3−i3i3-111-1−333−3i3−i3−i3i300000000000000000000
χ722-2-22-222-2-12i−2i−2i2i2-22i−2i−2i2i-22-1-11111-1-11−iii−i−iii−i1-10000-22−2i2i0000−333−3i−i−ii−i3i3i3−i3-111-13−3−33−i3i3i3−i300000000000000000000
χ732-2-22-222-2-1−2i2i2i−2i2-2−2i2i2i−2i-22-1-11111-1-11i−i−iii−i−ii1-100002-2−2i2i00003−3−33i−i−ii−i3i3i3−i31-1-113−3−33i3−i3−i3i300000000000000000000
χ742-2-22-222-2-1−2i2i2i−2i2-2−2i2i2i−2i-22-1-11111-1-11i−i−iii−i−ii1-100002-2−2i2i0000−333−3i−i−iii3−i3−i3i31-1-11−333−3−i3i3i3−i300000000000000000000
χ752-2-22-222-2-1−2i2i2i−2i2-2−2i2i2i−2i-22-1-11111-1-11i−i−iii−i−ii1-10000-222i−2i00003−3−33−iii−i−i3i3i3−i3-111-1−333−3−i3i3i3−i300000000000000000000
χ762-2-22-222-2-1−2i2i2i−2i2-2−2i2i2i−2i-22-1-11111-1-11i−i−iii−i−ii1-10000-222i−2i0000−333−3−iii−ii3−i3−i3i3-111-13−3−33i3−i3−i3i300000000000000000000
χ7744444444-24444-4-4-4-4-4-4-4-4-2-2-2-2-2-2-222-2-2-2-222222200000000000000000000000000000000000000000000000000000000
χ7844444444-2-4-4-4-4-4-44444-4-4-2-2-2-2-2-2-2222222-2-2-2-22200000000000000000000000000000000000000000000000000000000
χ79444-4-4-44-440000000000004-44-44-4-4000000000000000000000000000000000000000000000000000022−2222−22000000000000
χ80444-4-4-44-440000000000004-44-44-4-40000000000000000000000000000000000000000000000000000−2222−2222000000000000
χ8144-444-4-4-4-244-4-44444-4-4-4-42-2-2-2222-2-2-2-222-2-2222200000000000000000000000000000000000000000000000000000000
χ8244-444-4-4-4-2-4-44444-4-444-4-42-2-2-2222-2-222-2-222-2-22200000000000000000000000000000000000000000000000000000000
χ8344-4-4-44-444000000000000-4-44-4-444000000000000000000000000000000000000000000000000−2i22i2−2i22i20000000000000000
χ8444-4-4-44-444000000000000-4-44-4-4440000000000000000000000000000000000000000000000002i2−2i22i2−2i20000000000000000
χ854-444-4-4-44-24i−4i4i−4i4-44i−4i4i−4i4-42-222-2-22-22−2i2i−2i2i−2i2i−2i2i-2200000000000000000000000000000000000000000000000000000000
χ864-444-4-4-44-2−4i4i−4i4i4-4−4i4i−4i4i4-42-222-2-22-222i−2i2i−2i2i−2i2i−2i-2200000000000000000000000000000000000000000000000000000000
χ874-44-444-4-44000000000000-4-4-444-440000000000000000000000000000000000000000000000000000−2i22i22i2−2i2000000000000
χ884-44-444-4-44000000000000-4-4-444-4400000000000000000000000000000000000000000000000000002i2−2i2−2i22i2000000000000
χ894-4-44-444-4-24i−4i−4i4i-44−4i4i4i−4i4-4-2-22222-22-2−2i2i2i−2i2i−2i−2i2i-2200000000000000000000000000000000000000000000000000000000
χ904-4-44-444-4-2−4i4i4i−4i-444i−4i−4i4i4-4-2-22222-22-22i−2i−2i2i−2i2i2i−2i-2200000000000000000000000000000000000000000000000000000000
χ914-4-4-44-44440000000000004-4-44-44-4000000000000000000000000000000000000000000000000−2i22i22i2−2i20000000000000000
χ924-4-4-44-44440000000000004-4-44-44-40000000000000000000000000000000000000000000000002i2−2i2−2i22i20000000000000000
χ93888-8-8-88-8-4000000000000-44-44-44400000000000000000000000000000000000000000000000000000000000000000000
χ9488-8-8-88-88-400000000000044-444-4-400000000000000000000000000000000000000000000000000000000000000000000
χ958-88-888-8-8-4000000000000444-4-44-400000000000000000000000000000000000000000000000000000000000000000000
χ968-8-8-88-888-4000000000000-444-44-4400000000000000000000000000000000000000000000000000000000000000000000

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