Finite Group Databasebeta

← Group #11713977

Character table — Group #11713977

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74
size11111111222222222222666688888888888888888888888888888888121212121212242424242424242448484848
order12222222444444444444444436666666121212121212121212121212121212121212121212121212224444888888882444
χ111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111-1-1-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-111-1-1
χ4111111111111-1-1-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-11111-1-111
χ511111111-1-1-1-11111-1-1-1-1111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-1-11-1-11
χ611111111-1-1-1-11111-1-1-1-1111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-111-111-1
χ711111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-111-1-1-1-1111-11-1
χ811111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-11111-1-1-11-11
χ9222222222222222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1222222000000000000
χ10222222222222-2-2-2-2-2-2-2-22222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-2-222-2-2000000000000
χ1122222222-2-2-2-22222-2-2-2-22222-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-2-2-2-222000000000000
χ1222222222-2-2-2-2-2-2-2-222222222-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-122-2-2-2-2000000000000
χ13222-2-2-2-222i2i−2i−2i000000002-22-2222-2-22-2-22i2i2i2i−2i−2i−2i−2i0000000000000000002i−2i00000000000000
χ14222-2-2-2-222i2i−2i−2i000000002-22-2-1-1-111-111−i−i−i−iiiii3333−3−3−3−3−i3−i3−i3−i3i3i3i3i3002i−2i00000000000000
χ15222-2-2-2-222i2i−2i−2i000000002-22-2-1-1-111-111−i−i−i−iiiii−3−3−3−33333i3i3i3i3−i3−i3−i3−i3002i−2i00000000000000
χ16222-2-2-2-22−2i−2i2i2i000000002-22-2222-2-22-2-2−2i−2i−2i−2i2i2i2i2i000000000000000000−2i2i00000000000000
χ17222-2-2-2-22−2i−2i2i2i000000002-22-2-1-1-111-111iiii−i−i−i−i3333−3−3−3−3i3i3i3i3−i3−i3−i3−i300−2i2i00000000000000
χ18222-2-2-2-22−2i−2i2i2i000000002-22-2-1-1-111-111iiii−i−i−i−i−3−3−3−33333−i3−i3−i3−i3i3i3i3i300−2i2i00000000000000
χ1922-22-22-2-22-22-22i2i−2i−2i2i2i−2i−2i0000-11-11-111-111-1-111-1-1ii−i−iii−i−iii−i−iii−i−i000000−i2i2−i2i22−22−20000
χ2022-22-22-2-22-22-22i2i−2i−2i2i2i−2i−2i0000-11-11-111-111-1-111-1-1ii−i−iii−i−iii−i−iii−i−i000000i2−i2i2−i2−22−220000
χ2122-22-22-2-22-22-2−2i−2i2i2i−2i−2i2i2i0000-11-11-111-111-1-111-1-1−i−iii−i−iii−i−iii−i−iii000000−i2i2−i2i2−22−220000
χ2222-22-22-2-22-22-2−2i−2i2i2i−2i−2i2i2i0000-11-11-111-111-1-111-1-1−i−iii−i−iii−i−iii−i−iii000000i2−i2i2−i22−22−20000
χ2322-22-22-2-2-22-222i2i−2i−2i−2i−2i2i2i0000-11-11-111-1-1-111-1-111ii−i−iii−i−i−i−iii−i−iii000000−i2i2i2−i22−2−220000
χ2422-22-22-2-2-22-222i2i−2i−2i−2i−2i2i2i0000-11-11-111-1-1-111-1-111ii−i−iii−i−i−i−iii−i−iii000000i2−i2−i2i2−222−20000
χ2522-22-22-2-2-22-22−2i−2i2i2i2i2i−2i−2i0000-11-11-111-1-1-111-1-111−i−iii−i−iiiii−i−iii−i−i000000−i2i2i2−i2−222−20000
χ2622-22-22-2-2-22-22−2i−2i2i2i2i2i−2i−2i0000-11-11-111-1-1-111-1-111−i−iii−i−iiiii−i−iii−i−i000000i2−i2−i2i22−2−220000
χ272-2-222-2-2200002-22-20000-222-22-2-2-2-2222000000002-22-22-22-20000000000002-2000000000000
χ282-2-222-2-2200002-22-20000-222-2-11111-1-1-1−i3i3−i3i3−i3i3−i3i3-11-11-11-11−i3i3−i3i3−i3i3−i3i300002-2000000000000
χ292-2-222-2-2200002-22-20000-222-2-11111-1-1-1i3−i3i3−i3i3−i3i3−i3-11-11-11-11i3−i3i3−i3i3−i3i3−i300002-2000000000000
χ302-2-222-2-220000-22-220000-222-22-2-2-2-222200000000-22-22-22-22000000000000-22000000000000
χ312-2-222-2-220000-22-220000-222-2-11111-1-1-1−i3i3−i3i3−i3i3−i3i31-11-11-11-1i3−i3i3−i3i3−i3i3−i30000-22000000000000
χ322-2-222-2-220000-22-220000-222-2-11111-1-1-1i3−i3i3−i3i3−i3i3−i31-11-11-11-1−i3i3−i3i3−i3i3−i3i30000-22000000000000
χ332-2-2-2-2222000000002-22-2-2-2222-2-2222-2-200000000000000002-22-2-22-222-20000000000000000
χ342-2-2-2-2222000000002-22-2-2-222-111-1-1-1113−33−3−33−333−33−3−33−33-11-111-11-12-20000000000000000
χ352-2-2-2-2222000000002-22-2-2-222-111-1-1-111−33−333−33−3−33−333−33−3-11-111-11-12-20000000000000000
χ362-2-2-2-222200000000-22-22-2-2222-2-2222-2-20000000000000000-22-222-22-2-220000000000000000
χ372-2-2-2-222200000000-22-22-2-222-111-1-1-1113−33−3−33−33−33−333−33−31-11-1-11-11-220000000000000000
χ382-2-2-2-222200000000-22-22-2-222-111-1-1-111−33−333−33−33−33−3−33−331-11-1-11-11-220000000000000000
χ3933333333333333333333-1-1-1-100000000000000000000000000000000-1-1-1-1-1-111111111-1-1-1-1
χ4033333333333333333333-1-1-1-100000000000000000000000000000000-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ41333333333333-3-3-3-3-3-3-3-3-1-1-1-10000000000000000000000000000000011-1-1111111-1-1-1-1-1-111
χ42333333333333-3-3-3-3-3-3-3-3-1-1-1-10000000000000000000000000000000011-1-111-1-1-1-1111111-1-1
χ4333333333-3-3-3-33333-3-3-3-3-1-1-1-1000000000000000000000000000000001111-1-111-1-111-1-1-111-1
χ4433333333-3-3-3-33333-3-3-3-3-1-1-1-1000000000000000000000000000000001111-1-1-1-111-1-1111-1-11
χ4533333333-3-3-3-3-3-3-3-33333-1-1-1-100000000000000000000000000000000-1-1111111-1-1-1-111-11-11
χ4633333333-3-3-3-3-3-3-3-33333-1-1-1-100000000000000000000000000000000-1-11111-1-11111-1-11-11-1
χ4744-44-44-4-44-44-44i4i−4i−4i4i4i−4i−4i00001-11-11-1-11-1-111-1-111−i−iii−i−iii−i−iii−i−iii000000000000000000
χ4844-44-44-4-44-44-4−4i−4i4i4i−4i−4i4i4i00001-11-11-1-11-1-111-1-111ii−i−iii−i−iii−i−iii−i−i000000000000000000
χ4944-44-44-4-4-44-444i4i−4i−4i−4i−4i4i4i00001-11-11-1-1111-1-111-1-1−i−iii−i−iiiii−i−iii−i−i000000000000000000
χ5044-44-44-4-4-44-44−4i−4i4i4i4i4i−4i−4i00001-11-11-1-1111-1-111-1-1ii−i−iii−i−i−i−iii−i−iii000000000000000000
χ5144-4-44-44-44i−4i−4i4i0000000000001-111-1-11-1−i−iiiii−i−i−i3−i3i3i3i3i3−i3−i3−3−33333−3−3000000000000000000
χ5244-4-44-44-44i−4i−4i4i0000000000001-111-1-11-1−i−iiiii−i−ii3i3−i3−i3−i3−i3i3i333−3−3−3−333000000000000000000
χ5344-4-44-44-44i−4i−4i4i000000000000-22-2-222-222i2i−2i−2i−2i−2i2i2i0000000000000000000000000000000000
χ5444-4-44-44-4−4i4i4i−4i0000000000001-111-1-11-1ii−i−i−i−iii−i3−i3i3i3i3i3−i3−i333−3−3−3−333000000000000000000
χ5544-4-44-44-4−4i4i4i−4i0000000000001-111-1-11-1ii−i−i−i−iiii3i3−i3−i3−i3−i3i3i3−3−33333−3−3000000000000000000
χ5644-4-44-44-4−4i4i4i−4i000000000000-22-2-222-22−2i−2i2i2i2i2i−2i−2i0000000000000000000000000000000000
χ574-444-4-44-400004i−4i−4i4i0000000011-11-1-1-11−i3i3i3−i3−i3i3i3−i3−iii−i−iii−i3−3−333−3−33000000000000000000
χ584-444-4-44-400004i−4i−4i4i0000000011-11-1-1-11i3−i3−i3i3i3−i3−i3i3−iii−i−iii−i−333−3−333−3000000000000000000
χ594-444-4-44-400004i−4i−4i4i00000000-2-22-2222-2000000002i−2i−2i2i2i−2i−2i2i00000000000000000000000000
χ604-444-4-44-40000−4i4i4i−4i0000000011-11-1-1-11−i3i3i3−i3−i3i3i3−i3i−i−iii−i−ii−333−3−333−3000000000000000000
χ614-444-4-44-40000−4i4i4i−4i0000000011-11-1-1-11i3−i3−i3i3i3−i3−i3i3i−i−iii−i−ii3−3−333−3−33000000000000000000
χ624-444-4-44-40000−4i4i4i−4i00000000-2-22-2222-200000000−2i2i2i−2i−2i2i2i−2i00000000000000000000000000
χ634-44-444-4-4000000004i−4i−4i4i000011-1-11-11-13−3−33−333−3i3−i3−i3i3−i3i3i3−i3−iii−ii−i−ii000000000000000000
χ644-44-444-4-4000000004i−4i−4i4i000011-1-11-11-1−333−33−3−33−i3i3i3−i3i3−i3−i3i3−iii−ii−i−ii000000000000000000
χ654-44-444-4-4000000004i−4i−4i4i0000-2-222-22-2200000000000000002i−2i−2i2i−2i2i2i−2i000000000000000000
χ664-44-444-4-400000000−4i4i4i−4i000011-1-11-11-13−3−33−333−3−i3i3i3−i3i3−i3−i3i3i−i−ii−iii−i000000000000000000
χ674-44-444-4-400000000−4i4i4i−4i000011-1-11-11-1−333−33−3−33i3−i3−i3i3−i3i3i3−i3i−i−ii−iii−i000000000000000000
χ684-44-444-4-400000000−4i4i4i−4i0000-2-222-22-220000000000000000−2i2i2i−2i2i−2i−2i2i000000000000000000
χ69666-6-6-6-666i6i−6i−6i00000000-22-220000000000000000000000000000000000−2i2i00000000000000
χ70666-6-6-6-66−6i−6i6i6i00000000-22-2200000000000000000000000000000000002i−2i00000000000000
χ716-6-666-6-6600006-66-600002-2-22000000000000000000000000000000000000-22000000000000
χ726-6-666-6-660000-66-6600002-2-220000000000000000000000000000000000002-2000000000000
χ736-6-6-6-6666000000006-66-622-2-200000000000000000000000000000000-220000000000000000
χ746-6-6-6-666600000000-66-6622-2-2000000000000000000000000000000002-20000000000000000

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