Finite Group Databasebeta

← Group #10706346

Character table — Group #10706346

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75
size111122222222222244444444444444444888888888888888888888888161616161616242424242424242448484848
order122222344666666622224444466661212121244444466121212121212121212121212121212124412121212888888888888
χ1111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-111111111-1-1-1-1
χ411111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ5111111111111111111-1-1-11-1-1-111111111-111111-1-1-1-111111111-1-111-1-1-1-1-1-1-1-1iiii−i−i−i−iii−i−i
χ6111111111111111111-1-1-11-1-1-111111111-111111-1-1-1-111111111-1-111-1-1-1-1-1-1-1-1−i−i−i−iiiii−i−iii
χ7111111111111111111-1-1-11-1-1-111111111-11-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1111111iiii−i−i−i−i−i−iii
χ8111111111111111111-1-1-11-1-1-111111111-11-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1111111−i−i−i−iiiiiii−i−i
χ91111111-1-11111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-1-11111-1-1-1-11111-1-11-111-1-1ii−i−iii−i−ii−ii−i
χ101111111-1-11111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-1-11111-1-1-1-11111-1-11-111-1-1−i−iii−i−iii−ii−ii
χ111111111-1-11111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-1-1-111111111-1-1-11-1-111ii−i−iii−i−i−ii−ii
χ121111111-1-11111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-1-1-111111111-1-1-11-1-111−i−iii−i−iiii−ii−i
χ131111111-1-11111111-1-1-1-11-1111-1-1-1-1-1-1-1-1-1111-1-1-1-1111111-1-1-1-1-1-11111-11-1-11111-1-1-1-1111-1-11
χ141111111-1-11111111-1-1-1-11-1111-1-1-1-1-1-1-1-1-1111-1-1-1-1111111-1-1-1-1-1-11111-11-1-111-1-11111-1-1-111-1
χ151111111-1-11111111-1-1-1-11-1111-1-1-1-1-1-1-1-1-11-1-111-1-111-1-1-1-11111-1-111111-111-1-111-1-1-1-111-111-1
χ161111111-1-11111111-1-1-1-11-1111-1-1-1-1-1-1-1-1-11-1-111-1-111-1-1-1-11111-1-111111-111-1-1-1-11111-1-11-1-11
χ172222222222222222-2-222-2222-2-2-2-2-22222-2-2000022-2-200000000-2-2-2-222000000000000000000
χ182222222222222222-2-2-2-222-2-22-2-2-2-222222-20000-2-2220000000022-2-2-2-2000000000000000000
χ192222222-2-2222222222222-2-2-222222-2-2-2-2-2-20000222200000000-2-2-2-2-2-2000000000000000000
χ202222222-2-2222222222-2-2-2-222-22222-2-2-2-22-20000-2-2-2-20000000022-2-222000000000000000000
χ21222222-122-1-1-1-1-1-1-1222222222-1-1-1-1-1-1-1-1222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122-1-1-1-1000000000000
χ22222222-122-1-1-1-1-1-1-1222222222-1-1-1-1-1-1-1-122-2-2-2-2-1-1-1-111111111-1-1-1-1-1-1-2-21111000000000000
χ23222222-122-1-1-1-1-1-1-122-2-2-22-2-2-2-1-1-1-1-1-1-1-1-2222221111-1-1-1-1-1-1-1-111-1-111-2-21111000000000000
χ24222222-122-1-1-1-1-1-1-122-2-2-22-2-2-2-1-1-1-1-1-1-1-1-22-2-2-2-211111111111111-1-11122-1-1-1-1000000000000
χ25222222-122-1-1-1-1-1-1-1-2-222-2222-21111-1-1-1-1-2-20000-1-111−i3−i3i3i3−i3−i3i3i31111-1-100−i3i3−i3i3000000000000
χ26222222-122-1-1-1-1-1-1-1-2-222-2222-21111-1-1-1-1-2-20000-1-111i3i3−i3−i3i3i3−i3−i31111-1-100i3−i3i3−i3000000000000
χ27222222-122-1-1-1-1-1-1-1-2-2-2-222-2-221111-1-1-1-12-2000011-1-1−i3−i3i3i3−i3−i3i3i3-1-1111100i3−i3i3−i3000000000000
χ28222222-122-1-1-1-1-1-1-1-2-2-2-222-2-221111-1-1-1-12-2000011-1-1i3i3−i3−i3i3i3−i3−i3-1-1111100−i3i3−i3i3000000000000
χ29222222-1-2-2-1-1-1-1-1-1-122222-2-2-22-1-1-1-11111-2-20000-1-1-1-1−i3−i3i3i3i3i3−i3−i311111100−i3i3i3−i3000000000000
χ30222222-1-2-2-1-1-1-1-1-1-122222-2-2-22-1-1-1-11111-2-20000-1-1-1-1i3i3−i3−i3−i3−i3i3i311111100i3−i3−i3i3000000000000
χ31222222-1-2-2-1-1-1-1-1-1-122-2-2-2-222-2-1-1-1-111112-200001111−i3−i3i3i3i3i3−i3−i3-1-111-1-100i3−i3−i3i3000000000000
χ32222222-1-2-2-1-1-1-1-1-1-122-2-2-2-222-2-1-1-1-111112-200001111i3i3−i3−i3−i3−i3i3i3-1-111-1-100−i3i3i3−i3000000000000
χ33222222-1-2-2-1-1-1-1-1-1-1-2-222-2-2-2-2-2111111112222-2-2-1-111-1-1-1-11111-1-1-1-1112-2-1-111000000000000
χ34222222-1-2-2-1-1-1-1-1-1-1-2-222-2-2-2-2-21111111122-2-222-1-1111111-1-1-1-1-1-1-1-111-2211-1-1000000000000
χ35222222-1-2-2-1-1-1-1-1-1-1-2-2-2-22-222211111111-2222-2-211-1-1-1-1-1-1111111-1-1-1-1-2211-1-1000000000000
χ36222222-1-2-2-1-1-1-1-1-1-1-2-2-2-22-222211111111-22-2-22211-1-11111-1-1-1-111-1-1-1-12-2-1-111000000000000
χ3722-2-22-2200222-2-2-2-22-22-22000-222-2-200000000002-22-2000000000000000000002−22−22−22−20000
χ3822-2-22-2200222-2-2-2-22-22-22000-222-2-200000000002-22-200000000000000000000−22−22−22−220000
χ3922-2-22-2200222-2-2-2-22-2-22-2000222-2-20000000000-22-2200000000000000000000−i2i2−i2i2i2−i2i2−i20000
χ4022-2-22-2200222-2-2-2-22-2-22-2000222-2-20000000000-22-2200000000000000000000i2−i2i2−i2−i2i2−i2i20000
χ4122-2-22-2200222-2-2-2-2-222-2-20002-2-22200000000002-2-2200000000000000000000−i2i2i2−i2−i2i2i2−i20000
χ4222-2-22-2200222-2-2-2-2-222-2-20002-2-22200000000002-2-2200000000000000000000i2−i2−i2i2i2−i2−i2i20000
χ4322-2-22-2200222-2-2-2-2-22-222000-2-2-2220000000000-222-2000000000000000000002−2−22−222−20000
χ4422-2-22-2200222-2-2-2-2-22-222000-2-2-2220000000000-222-200000000000000000000−222−22−2−220000
χ454444-4-4444-4-44-4-44400000-4000000044-4-4000000000000000000000000000000000000000000
χ464444-4-44-4-4-4-44-4-4440000040000000-4-444000000000000000000000000000000000000000000
χ474444-4-4-24422-222-2-200000-4000−2i32i3−2i32i3-2-22200000000000000000000−2i32i300000000000000000000
χ484444-4-4-24422-222-2-200000-40002i3−2i32i3−2i3-2-222000000000000000000002i3−2i300000000000000000000
χ494444-4-4-2-4-422-222-2-2000004000−2i32i3−2i32i322-2-2000000000000000000002i3−2i300000000000000000000
χ504444-4-4-2-4-422-222-2-20000040002i3−2i32i3−2i322-2-200000000000000000000−2i32i300000000000000000000
χ5144-4-44-4-200-2-2-222224-44-44000-4-2-2220000000000-22-2200000000000000000000000000000000
χ5244-4-44-4-200-2-2-222224-4-44-40004-2-22200000000002-22-200000000000000000000000000000000
χ5344-4-44-4-200-2-2-22222-444-4-4000422-2-20000000000-222-200000000000000000000000000000000
χ5444-4-44-4-200-2-2-22222-44-444000-422-2-200000000002-2-2200000000000000000000000000000000
χ5544-4-4-44400-4-4444-4-40000004i−4i00000000000000000000000000000004i−4i000000000000000000
χ5644-4-4-44400-4-4444-4-4000000−4i4i0000000000000000000000000000000−4i4i000000000000000000
χ5744-4-4-44-20022-2-2-2220000004i−4i0−2i32i32i3−2i3000000000000000000000023−2300−2i2i000000000000000000
χ5844-4-4-44-20022-2-2-2220000004i−4i02i3−2i3−2i32i30000000000000000000000−232300−2i2i000000000000000000
χ5944-4-4-44-20022-2-2-222000000−4i4i0−2i32i32i3−2i30000000000000000000000−2323002i−2i000000000000000000
χ6044-4-4-44-20022-2-2-222000000−4i4i02i3−2i3−2i32i3000000000000000000000023−23002i−2i000000000000000000
χ614-44-40044i−4i00-4004-400000000000004i−4i00002-22i−2i00002-22-22i−2i2i−2i000000000000000000000000
χ624-44-40044i−4i00-4004-400000000000004i−4i0000-22−2i2i0000-22-22−2i2i−2i2i000000000000000000000000
χ634-44-4004−4i4i00-4004-40000000000000−4i4i00002-2−2i2i00002-22-2−2i2i−2i2i000000000000000000000000
χ644-44-4004−4i4i00-4004-40000000000000−4i4i0000-222i−2i0000-22-222i−2i2i−2i000000000000000000000000
χ654-44-400-24i−4i−2i32i32−2i32i3-220000000000000−2i2i23−23002-22i−2i0000−1−i31+i3−1+i31−i32ζ22−2ζ222ζ14−2ζ14000000000000000000000000
χ664-44-400-24i−4i−2i32i32−2i32i3-220000000000000−2i2i23−2300-22−2i2i00001+i3−1−i31−i3−1+i3−2ζ222ζ22−2ζ142ζ14000000000000000000000000
χ674-44-400-24i−4i2i3−2i322i3−2i3-220000000000000−2i2i−2323002-22i−2i0000−1+i31−i3−1−i31+i32ζ14−2ζ142ζ22−2ζ22000000000000000000000000
χ684-44-400-24i−4i2i3−2i322i3−2i3-220000000000000−2i2i−232300-22−2i2i00001−i3−1+i31+i3−1−i3−2ζ142ζ14−2ζ222ζ22000000000000000000000000
χ694-44-400-2−4i4i−2i32i32−2i32i3-2200000000000002i−2i−2323002-2−2i2i0000−1−i31+i3−1+i31−i3−2ζ222ζ22−2ζ142ζ14000000000000000000000000
χ704-44-400-2−4i4i−2i32i32−2i32i3-2200000000000002i−2i−232300-222i−2i00001+i3−1−i31−i3−1+i32ζ22−2ζ222ζ14−2ζ14000000000000000000000000
χ714-44-400-2−4i4i2i3−2i322i3−2i3-2200000000000002i−2i23−23002-2−2i2i0000−1+i31−i3−1−i31+i3−2ζ142ζ14−2ζ222ζ22000000000000000000000000
χ724-44-400-2−4i4i2i3−2i322i3−2i3-2200000000000002i−2i23−2300-222i−2i00001−i3−1+i31+i3−1−i32ζ14−2ζ142ζ22−2ζ22000000000000000000000000
χ738-8-880080000-800-8800000000000000000000000000000000000000000000000000000000000
χ748-8-8800-400−4i34i344i3−4i34-400000000000000000000000000000000000000000000000000000000000
χ758-8-8800-4004i3−4i34−4i34i34-400000000000000000000000000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 24 (ζ24 = 1); i = ζ6.