Finite Group Databasebeta

← Group #10695931

Character table — Group #10695931

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75
size111122222222222222224444444444488888888888888888888888888161616161616242424242424242448484848
order12222234444446666666444121212121212121222444444666612121212121212121212121212124412121212888888882488
χ1111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111-1-111-1-1111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1
χ4111111111111111111111111111111111-1-111-1-1111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ51111111111111111111111111111111-1-111-1-111-1-1-1-1111111-1-1-1-11111-1-1-1-1-1-11111-1-1-1-1-1-111
χ61111111111111111111111111111111-1-111-1-111-1-1-1-1111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1111111-1-1
χ71111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-111-1-1
χ81111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-111
χ92222222222-2-222222222-2-2-22222-2-2-2-22200-2-2002222-2-20000-2-2-2-20000000000000000000000
χ102222222222-2-222222222-2-2-22222-2-2-2-2-2-2002200-2-2-2-2-2-2000022220000000000000000000000
χ112222222-2-2-222-22222222-22-2-2-2-2-22222000000000000-2-20000000000002-222-2-2000000000000
χ122222222-2-2-222-22222222-22-2-2-2-2-22222000000000000-2-2000000000000-22-2-222000000000000
χ132222222-2-2-2-2-2-222222222-22-2-2-2-2-2-2-2-2002200-2-200002222220000-2-2-2-2000000000000000000
χ142222222-2-2-2-2-2-222222222-22-2-2-2-2-2-2-2-200-2-20022000022-2-2-2-200002222000000000000000000
χ15222222-1222222-1-1-1-1-1-1-1222-1-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122-1-1-1-1000000000000
χ16222222-1222222-1-1-1-1-1-1-1222-1-1-1-1-1-1-1-122-2-222-2-2-1-1-1-1-1-11111-1-1-1-11111-2-21111000000000000
χ17222222-1222222-1-1-1-1-1-1-1222-1-1-1-1-1-1-1-1-2-222-2-2221111-1-1-1-1-1-11111-1-1-1-1-2-21111000000000000
χ18222222-1222222-1-1-1-1-1-1-1222-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-21111-1-111111111111122-1-1-1-1000000000000
χ19222222-1222-2-22-1-1-1-1-1-1-1-2-2-2-1-1-1-111112200-2-200-1-1-1-111−i3−i3i3i31111−i3−i3i3i300−i3i3−i3i3000000000000
χ20222222-1222-2-22-1-1-1-1-1-1-1-2-2-2-1-1-1-111112200-2-200-1-1-1-111i3i3−i3−i31111i3i3−i3−i300i3−i3i3−i3000000000000
χ21222222-1222-2-22-1-1-1-1-1-1-1-2-2-2-1-1-1-11111-2-2002200111111−i3−i3i3i3-1-1-1-1−i3−i3i3i300i3−i3i3−i3000000000000
χ22222222-1222-2-22-1-1-1-1-1-1-1-2-2-2-1-1-1-11111-2-2002200111111i3i3−i3−i3-1-1-1-1i3i3−i3−i300−i3i3−i3i3000000000000
χ23222222-1-2-2-222-2-1-1-1-1-1-1-1-22-21111-1-1-1-100000000−i3−i3i3i311−i3−i3i3i3−i3−i3i3i3i3i3−i3−i32-2-1-111000000000000
χ24222222-1-2-2-222-2-1-1-1-1-1-1-1-22-21111-1-1-1-100000000−i3−i3i3i311i3i3−i3−i3−i3−i3i3i3−i3−i3i3i3-2211-1-1000000000000
χ25222222-1-2-2-222-2-1-1-1-1-1-1-1-22-21111-1-1-1-100000000i3i3−i3−i311−i3−i3i3i3i3i3−i3−i3i3i3−i3−i3-2211-1-1000000000000
χ26222222-1-2-2-222-2-1-1-1-1-1-1-1-22-21111-1-1-1-100000000i3i3−i3−i311i3i3−i3−i3i3i3−i3−i3−i3−i3i3i32-2-1-111000000000000
χ27222222-1-2-2-2-2-2-2-1-1-1-1-1-1-12-2211111111002200-2-2−i3−i3i3i3-1-1-1-1-1-1i3i3−i3−i3111100−i3i3i3−i3000000000000
χ28222222-1-2-2-2-2-2-2-1-1-1-1-1-1-12-2211111111002200-2-2i3i3−i3−i3-1-1-1-1-1-1−i3−i3i3i3111100i3−i3−i3i3000000000000
χ29222222-1-2-2-2-2-2-2-1-1-1-1-1-1-12-221111111100-2-20022−i3−i3i3i3-1-11111i3i3−i3−i3-1-1-1-100i3−i3−i3i3000000000000
χ30222222-1-2-2-2-2-2-2-1-1-1-1-1-1-12-221111111100-2-20022i3i3−i3−i3-1-11111−i3−i3i3i3-1-1-1-100−i3i3i3−i3000000000000
χ312222-2-2222-222-2-2-22-2-222-2-2222-2-222-2-20000000000002-2000000000000000000000022-2-20000
χ322222-2-2222-222-2-2-22-2-222-2-2222-2-222-2-20000000000002-20000000000000000000000-2-2220000
χ332222-2-2222-2-2-2-2-2-22-2-22222-222-2-2-2-222000000000000-220000000000000000002i2i−2i−2i00000000
χ342222-2-2222-2-2-2-2-2-22-2-22222-222-2-2-2-222000000000000-22000000000000000000−2i−2i2i2i00000000
χ352222-2-22-2-22222-2-22-2-2222-2-2-2-22222-2-2000000000000-2200000000000000000000000000002-2
χ362222-2-22-2-22222-2-22-2-2222-2-2-2-22222-2-2000000000000-220000000000000000000000000000-22
χ372222-2-22-2-22-2-22-2-22-2-222-222-2-222-2-2220000000000002-2000000000000000000000000002-200
χ382222-2-22-2-22-2-22-2-22-2-222-222-2-222-2-2220000000000002-200000000000000000000000000-2200
χ392-2-222-222-2-2002222-2-2-2-20002-22-200002-20000002-22-200000000000000000000−i2i2−i2i2−i2i2−i2i20000
χ402-2-222-222-2-2002222-2-2-2-20002-22-200002-20000002-22-200000000000000000000i2−i2i2−i2i2−i2i2−i20000
χ412-2-222-222-2-2002222-2-2-2-20002-22-20000-22000000-22-2200000000000000000000−i2i2−i2i2i2−i2i2−i20000
χ422-2-222-222-2-2002222-2-2-2-20002-22-20000-22000000-22-2200000000000000000000i2−i2i2−i2−i2i2−i2i20000
χ432-2-22-2222-2200-2-2-2222-2-20002-2-22000000002i−2i0000000000002i−2i2i−2i00000000002−2−22−i2i2i2−i20000
χ442-2-22-2222-2200-2-2-2222-2-20002-2-22000000002i−2i0000000000002i−2i2i−2i0000000000−222−2i2−i2−i2i20000
χ452-2-22-2222-2200-2-2-2222-2-20002-2-2200000000−2i2i000000000000−2i2i−2i2i00000000002−2−22i2−i2−i2i20000
χ462-2-22-2222-2200-2-2-2222-2-20002-2-2200000000−2i2i000000000000−2i2i−2i2i0000000000−222−2−i2i2i2−i20000
χ474444-4-4-244-444-422-222-2-2-4-44-2-222-2-222000000000000-22000000000000000000000000000000
χ484444-4-4-244-4-4-4-422-222-2-244-4-2-22222-2-20000000000002-2000000000000000000000000000000
χ494444-4-4-2-4-4444422-222-2-24-4-422-2-2-2-2220000000000002-2000000000000000000000000000000
χ504444-4-4-2-4-44-4-4422-222-2-2-44422-2-222-2-2000000000000-22000000000000000000000000000000
χ5144-4-40040004i−4i000-4004-400000004i−4i00002-2002i−2i0000002-22-200002i−2i2i−2i000000000000000000
χ5244-4-40040004i−4i000-4004-400000004i−4i0000-2200−2i2i000000-22-220000−2i2i−2i2i000000000000000000
χ5344-4-4004000−4i4i000-4004-40000000−4i4i00002-200−2i2i0000002-22-20000−2i2i−2i2i000000000000000000
χ5444-4-4004000−4i4i000-4004-40000000−4i4i0000-22002i−2i000000-22-2200002i−2i2i−2i000000000000000000
χ5544-4-400-20004i−4i0−2i32i32−2i32i3-220000000−2i2i23−23002-2002i−2i000000−1−i31+i3−1+i31−i300002ζ14−2ζ142ζ22−2ζ22000000000000000000
χ5644-4-400-20004i−4i0−2i32i32−2i32i3-220000000−2i2i23−2300-2200−2i2i0000001+i3−1−i31−i3−1+i30000−2ζ142ζ14−2ζ222ζ22000000000000000000
χ5744-4-400-20004i−4i02i3−2i322i3−2i3-220000000−2i2i−2323002-2002i−2i000000−1+i31−i3−1−i31+i300002ζ22−2ζ222ζ14−2ζ14000000000000000000
χ5844-4-400-20004i−4i02i3−2i322i3−2i3-220000000−2i2i−232300-2200−2i2i0000001−i3−1+i31+i3−1−i30000−2ζ222ζ22−2ζ142ζ14000000000000000000
χ5944-4-400-2000−4i4i0−2i32i32−2i32i3-2200000002i−2i−2323002-200−2i2i000000−1−i31+i3−1+i31−i30000−2ζ142ζ14−2ζ222ζ22000000000000000000
χ6044-4-400-2000−4i4i0−2i32i32−2i32i3-2200000002i−2i−232300-22002i−2i0000001+i3−1−i31−i3−1+i300002ζ14−2ζ142ζ22−2ζ22000000000000000000
χ6144-4-400-2000−4i4i02i3−2i322i3−2i3-2200000002i−2i23−23002-200−2i2i000000−1+i31−i3−1−i31+i30000−2ζ222ζ22−2ζ142ζ14000000000000000000
χ6244-4-400-2000−4i4i02i3−2i322i3−2i3-2200000002i−2i23−2300-22002i−2i0000001−i3−1+i31+i3−1−i300002ζ22−2ζ222ζ14−2ζ14000000000000000000
χ634-4-444-44-44400-4444-4-4-4-4000-44-44000000000000000000000000000000000000000000000000
χ644-4-444-4-24-4-4004-2-2-22222000-22-2200004-4000000-22-2200000000000000000000000000000000
χ654-4-444-4-24-4-4004-2-2-22222000-22-220000-440000002-22-200000000000000000000000000000000
χ664-4-444-4-2-44400-4-2-2-222220002-22-2000000000000−2i32i32i3−2i300000000000000000000000000000000
χ674-4-444-4-2-44400-4-2-2-222220002-22-20000000000002i3−2i3−2i32i300000000000000000000000000000000
χ684-4-44-444-44-4004-4-4444-4-4000-444-4000000000000000000000000000000000000000000000000
χ694-4-44-44-24-4400-422-2-2-222000-222-2000000004i−4i000000000000−2i2i−2i2i0000000000000000000000
χ704-4-44-44-24-4400-422-2-2-222000-222-200000000−4i4i0000000000002i−2i2i−2i0000000000000000000000
χ714-4-44-44-2-44-400422-2-2-2220002-2-22000000000000000000000023−23−23230000000000000000000000
χ724-4-44-44-2-44-400422-2-2-2220002-2-220000000000000000000000−232323−230000000000000000000000
χ738-88-800800000000-800-880000000000000000000000000000000000000000000000000000000
χ748-88-800-4000000−4i34i344i3−4i34-40000000000000000000000000000000000000000000000000000000
χ758-88-800-40000004i3−4i34−4i34i34-40000000000000000000000000000000000000000000000000000000

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