Finite Group Databasebeta

← Group #11714083

Character table — Group #11714083

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74
size11111111222222222222666688888888888888888888888888888888121212121212242424242424242448484848
order12222222444444444444444436666666121212121212121212121212121212121212121212121212444444888888882444
χ111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111-1-1-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-111-1-1
χ4111111111111-1-1-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11111-1-111
χ511111111-1-1-1-11111-1-1-1-1111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111-1-111-1-111-1-11-11-1
χ611111111-1-1-1-11111-1-1-1-1111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-111-1-111-11-11
χ711111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1111-1-11
χ811111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111-1-11111-1-1-111-1
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
χ10222222222222-2-2-2-2-2-2-2-22222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111111122-2-2-2-2000000000000
χ1122222222-2-2-2-22222-2-2-2-22222-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-2-222-2-2000000000000
χ1222222222-2-2-2-2-2-2-2-222222222-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-2-2-2-222000000000000
χ13222-2-22-2-2000000002i2i−2i−2i22-2-2222-2-22-2-200000000000000002i2i2i2i−2i−2i−2i−2i00002i−2i000000000000
χ14222-2-22-2-2000000002i2i−2i−2i22-2-2-1-1-111-111−i3−i3−i3−i3i3i3i3i33333−3−3−3−3−i−i−i−iiiii00002i−2i000000000000
χ15222-2-22-2-2000000002i2i−2i−2i22-2-2-1-1-111-111i3i3i3i3−i3−i3−i3−i3−3−3−3−33333−i−i−i−iiiii00002i−2i000000000000
χ16222-2-22-2-200000000−2i−2i2i2i22-2-2222-2-22-2-20000000000000000−2i−2i−2i−2i2i2i2i2i0000−2i2i000000000000
χ17222-2-22-2-200000000−2i−2i2i2i22-2-2-1-1-111-111−i3−i3−i3−i3i3i3i3i3−3−3−3−33333iiii−i−i−i−i0000−2i2i000000000000
χ18222-2-22-2-200000000−2i−2i2i2i22-2-2-1-1-111-111i3i3i3i3−i3−i3−i3−i33333−3−3−3−3iiii−i−i−i−i0000−2i2i000000000000
χ1922-22-2-22-200002i2i−2i−2i00002-22-222-22-2-22-2000000002i2i−2i−2i2i2i−2i−2i00000000002i−2i00000000000000
χ2022-22-2-22-200002i2i−2i−2i00002-22-2-1-11-111-1133−3−333−3−3−i−iii−i−iii−i3−i3i3i3−i3−i3i3i3002i−2i00000000000000
χ2122-22-2-22-200002i2i−2i−2i00002-22-2-1-11-111-11−3−333−3−333−i−iii−i−iiii3i3−i3−i3i3i3−i3−i3002i−2i00000000000000
χ2222-22-2-22-20000−2i−2i2i2i00002-22-222-22-2-22-200000000−2i−2i2i2i−2i−2i2i2i0000000000−2i2i00000000000000
χ2322-22-2-22-20000−2i−2i2i2i00002-22-2-1-11-111-1133−3−333−3−3ii−i−iii−i−ii3i3−i3−i3i3i3−i3−i300−2i2i00000000000000
χ2422-22-2-22-20000−2i−2i2i2i00002-22-2-1-11-111-11−3−333−3−333ii−i−iii−i−i−i3−i3i3i3−i3−i3i3i300−2i2i00000000000000
χ2522-2-22-2-222i2i−2i−2i000000002-2-2222-2-22-2-222i2i−2i−2i−2i−2i2i2i00000000000000002i−2i0000000000000000
χ2622-2-22-2-222i2i−2i−2i000000002-2-22-1-111-111-1−i−iiiii−i−i−i3−i3i3i3i3i3−i3−i3−3−33333−3−32i−2i0000000000000000
χ2722-2-22-2-222i2i−2i−2i000000002-2-22-1-111-111-1−i−iiiii−i−ii3i3−i3−i3−i3−i3i3i333−3−3−3−3332i−2i0000000000000000
χ2822-2-22-2-22−2i−2i2i2i000000002-2-2222-2-22-2-22−2i−2i2i2i2i2i−2i−2i0000000000000000−2i2i0000000000000000
χ2922-2-22-2-22−2i−2i2i2i000000002-2-22-1-111-111-1ii−i−i−i−iii−i3−i3i3i3i3i3−i3−i333−3−3−3−333−2i2i0000000000000000
χ3022-2-22-2-22−2i−2i2i2i000000002-2-22-1-111-111-1ii−i−i−i−iiii3i3−i3−i3−i3−i3i3i3−3−33333−3−3−2i2i0000000000000000
χ312-2-2-2-22222-22-22-22-22-22-20000-11111-1-1-11-11-11-11-11-11-11-11-11-11-11-11-1000000−i2i2−i2i2−i2i2−i2i20000
χ322-2-2-2-22222-22-22-22-22-22-20000-11111-1-1-11-11-11-11-11-11-11-11-11-11-11-11-1000000i2−i2i2−i2i2−i2i2−i20000
χ332-2-2-2-22222-22-2-22-22-22-220000-11111-1-1-11-11-11-11-1-11-11-11-11-11-11-11-11000000−i2i2−i2i2i2−i2i2−i20000
χ342-2-2-2-22222-22-2-22-22-22-220000-11111-1-1-11-11-11-11-1-11-11-11-11-11-11-11-11000000i2−i2i2−i2−i2i2−i2i20000
χ352-2-2-2-2222-22-222-22-2-22-220000-11111-1-1-1-11-11-11-111-11-11-11-1-11-11-11-11000000−i2i2i2−i2−i2i2i2−i20000
χ362-2-2-2-2222-22-222-22-2-22-220000-11111-1-1-1-11-11-11-111-11-11-11-1-11-11-11-11000000i2−i2−i2i2i2−i2−i2i20000
χ372-2-2-2-2222-22-22-22-222-22-20000-11111-1-1-1-11-11-11-11-11-11-11-111-11-11-11-1000000−i2i2i2−i2i2−i2−i2i20000
χ382-2-2-2-2222-22-22-22-222-22-20000-11111-1-1-1-11-11-11-11-11-11-11-111-11-11-11-1000000i2−i2−i2i2−i2i2i2−i20000
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
χ41333333333333-3-3-3-3-3-3-3-3-1-1-1-100000000000000000000000000000000-1-111111111-1-1-1-1-1-111
χ42333333333333-3-3-3-3-3-3-3-3-1-1-1-100000000000000000000000000000000-1-11111-1-1-1-1111111-1-1
χ4333333333-3-3-3-33333-3-3-3-3-1-1-1-10000000000000000000000000000000011-1-11111-1-111-1-1-11-11
χ4433333333-3-3-3-33333-3-3-3-3-1-1-1-10000000000000000000000000000000011-1-111-1-111-1-1111-11-1
χ4533333333-3-3-3-3-3-3-3-33333-1-1-1-1000000000000000000000000000000001111-1-111-1-1-1-111-111-1
χ4633333333-3-3-3-3-3-3-3-33333-1-1-1-1000000000000000000000000000000001111-1-1-1-11111-1-11-1-11
χ474-444-4-4-444i−4i−4i4i0000000000001-111-1-1-11−iii−ii−i−ii−i3i3i3−i3i3−i3−i3i3−333−33−3−33000000000000000000
χ484-444-4-4-444i−4i−4i4i0000000000001-111-1-1-11−iii−ii−i−iii3−i3−i3i3−i3i3i3−i33−3−33−333−3000000000000000000
χ494-444-4-4-444i−4i−4i4i000000000000-22-2-2222-22i−2i−2i2i−2i2i2i−2i0000000000000000000000000000000000
χ504-444-4-4-44−4i4i4i−4i0000000000001-111-1-1-11i−i−ii−iii−i−i3i3i3−i3i3−i3−i3i33−3−33−333−3000000000000000000
χ514-444-4-4-44−4i4i4i−4i0000000000001-111-1-1-11i−i−ii−iii−ii3−i3−i3i3−i3i3i3−i3−333−33−3−33000000000000000000
χ524-444-4-4-44−4i4i4i−4i000000000000-22-2-2222-2−2i2i2i−2i2i−2i−2i2i0000000000000000000000000000000000
χ534-44-44-44-400004i−4i−4i4i000000001-11-11-11-13−3−333−3−33−iii−i−iii−i−i3i3i3−i3−i3i3i3−i3000000000000000000
χ544-44-44-44-400004i−4i−4i4i000000001-11-11-11-1−333−3−333−3−iii−i−iii−ii3−i3−i3i3i3−i3−i3i3000000000000000000
χ554-44-44-44-400004i−4i−4i4i00000000-22-22-22-22000000002i−2i−2i2i2i−2i−2i2i00000000000000000000000000
χ564-44-44-44-40000−4i4i4i−4i000000001-11-11-11-13−3−333−3−33i−i−iii−i−iii3−i3−i3i3i3−i3−i3i3000000000000000000
χ574-44-44-44-40000−4i4i4i−4i000000001-11-11-11-1−333−3−333−3i−i−iii−i−ii−i3i3i3−i3−i3i3i3−i3000000000000000000
χ584-44-44-44-40000−4i4i4i−4i00000000-22-22-22-2200000000−2i2i2i−2i−2i2i2i−2i00000000000000000000000000
χ594-4-4444-4-4000000004i−4i−4i4i00001-1-1111-1-1−i3i3−i3i3i3−i3i3−i33−33−3−33−33−ii−iii−ii−i000000000000000000
χ604-4-4444-4-4000000004i−4i−4i4i00001-1-1111-1-1i3−i3i3−i3−i3i3−i3i3−33−333−33−3−ii−iii−ii−i000000000000000000
χ614-4-4444-4-4000000004i−4i−4i4i0000-222-2-2-22200000000000000002i−2i2i−2i−2i2i−2i2i000000000000000000
χ624-4-4444-4-400000000−4i4i4i−4i00001-1-1111-1-1−i3i3−i3i3i3−i3i3−i3−33−333−33−3i−ii−i−ii−ii000000000000000000
χ634-4-4444-4-400000000−4i4i4i−4i00001-1-1111-1-1i3−i3i3−i3−i3i3−i3i33−33−3−33−33i−ii−i−ii−ii000000000000000000
χ644-4-4444-4-400000000−4i4i4i−4i0000-222-2-2-2220000000000000000−2i2i−2i2i2i−2i2i−2i000000000000000000
χ654-4-4-4-44444-44-44-44-44-44-400001-1-1-1-1111-11-11-11-11-11-11-11-11-11-11-11-11000000000000000000
χ664-4-4-4-44444-44-4-44-44-44-4400001-1-1-1-1111-11-11-11-111-11-11-11-11-11-11-11-1000000000000000000
χ674-4-4-4-4444-44-444-44-4-44-4400001-1-1-1-11111-11-11-11-1-11-11-11-111-11-11-11-1000000000000000000
χ684-4-4-4-4444-44-44-44-444-44-400001-1-1-1-11111-11-11-11-11-11-11-11-1-11-11-11-11000000000000000000
χ69666-6-66-6-6000000006i6i−6i−6i-2-222000000000000000000000000000000000000−2i2i000000000000
χ70666-6-66-6-600000000−6i−6i6i6i-2-2220000000000000000000000000000000000002i−2i000000000000
χ7166-66-6-66-600006i6i−6i−6i0000-22-220000000000000000000000000000000000−2i2i00000000000000
χ7266-66-6-66-60000−6i−6i6i6i0000-22-2200000000000000000000000000000000002i−2i00000000000000
χ7366-6-66-6-666i6i−6i−6i00000000-222-200000000000000000000000000000000−2i2i0000000000000000
χ7466-6-66-6-66−6i−6i6i6i00000000-222-2000000000000000000000000000000002i−2i0000000000000000

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