Finite Group Databasebeta

← Group #10768809

Character table — Group #10768809

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78
size111122222222222222444444444444888888888888888888888888888888161616162424242424242424242424244848
order122222223446666666244466661212121222444444444412121212121212121212121212121212121266121222244444888888
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1
χ41111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111
χ5111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-111-1-111-1-11111-1-1
χ6111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-111-1-111-1-1-1-111
χ7111111111111111111111111111111-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-1-1-111
χ8111111111111111111111111111111-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1111111-1-1
χ91111-1-1111-1-11111111-1-111-1-1-1-1-1-1-1-11-11-111-1-111-1-11111-1-1-1-1111111-1-1-1-11-11-11-11-11-11-111-1-11-1
χ101111-1-1111-1-11111111-1-111-1-1-1-1-1-1-1-11-11-111-1-111-1-11111-1-1-1-1111111-1-1-1-11-11-1-11-11-11-11-1-111-11
χ111111-1-1111-1-11111111-1-111-1-1-1-1-1-1-1-11-11-1-1-111-1-111-1-1-1-1111111-1-1-1-111111-11-11-11-11-11-1-1-111-11
χ121111-1-1111-1-11111111-1-111-1-1-1-1-1-1-1-11-11-1-1-111-1-111-1-1-1-1111111-1-1-1-111111-11-1-11-11-11-1111-1-11-1
χ131111-1-1111-1-11111111-1-111-1-1-1-1-1-1-1-1-11-1111-1-1-1-111-1-1-1-11111111111-1-1-1-1-11-111-1-111-1-1111-1-1-11
χ141111-1-1111-1-11111111-1-111-1-1-1-1-1-1-1-1-11-1111-1-1-1-111-1-1-1-11111111111-1-1-1-1-11-11-111-1-111-1-1-1111-1
χ151111-1-1111-1-11111111-1-111-1-1-1-1-1-1-1-1-11-11-1-11111-1-11111-1-1-1-111-1-1-1-11111-11-111-1-111-1-11-1-1111-1
χ161111-1-1111-1-11111111-1-111-1-1-1-1-1-1-1-1-11-11-1-11111-1-11111-1-1-1-111-1-1-1-11111-11-11-111-1-111-111-1-1-11
χ17222222222-2-222222222-2-2-22222-2-2-2-22-2-220000000000000000-2-2000000002-2-2200000000000000
χ18222222222-2-222222222-2-2-22222-2-2-2-2-222-20000000000000000-2-200000000-222-200000000000000
χ1922222222-122-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-100000000000000
χ2022222222-122-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-12222-2-2-2-2-2-2-2-211111111-1-111111111-1-1-1-100000000000000
χ2122222222-122-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-2-2-2-22222-2-2-2-211111111-1-1-1-1-1-1-1-1-1-1111100000000000000
χ2222222222-122-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-22222-1-1-1-1-1-1-1-1-1-111111111111100000000000000
χ2322222222-1-2-2-1-1-1-1-1-1-12-2-2-2-1-1-1-111112-2-2200000000−i3−i3i3i3−i3−i3i3i311−i3−i3i3i3−i3−i3i3i3-111-100000000000000
χ2422222222-1-2-2-1-1-1-1-1-1-12-2-2-2-1-1-1-111112-2-2200000000i3i3−i3−i3i3i3−i3−i311i3i3−i3−i3i3i3−i3−i3-111-100000000000000
χ2522222222-1-2-2-1-1-1-1-1-1-12-2-2-2-1-1-1-11111-222-200000000−i3−i3i3i3−i3−i3i3i311i3i3−i3−i3i3i3−i3−i31-1-1100000000000000
χ2622222222-1-2-2-1-1-1-1-1-1-12-2-2-2-1-1-1-11111-222-200000000i3i3−i3−i3i3i3−i3−i311−i3−i3i3i3−i3−i3i3i31-1-1100000000000000
χ27222222-2-22222-2-2-2-222-2-22-222-2-222-2-2000000000000000000002-20000000000002200-2-200000000
χ28222222-2-22222-2-2-2-222-2-22-222-2-222-2-2000000000000000000002-2000000000000-2-2002200000000
χ29222222-2-22-2-22-2-2-2-222-22-2222-2-2-2-22200000000000000000000-22000000000000002-200-22000000
χ30222222-2-22-2-22-2-2-2-222-22-2222-2-2-2-22200000000000000000000-2200000000000000-22002-2000000
χ312222-2-2222222222222-22-2-2-2-2-2-2222222-2-20000000000000000-2-20000000022-2-200000000000000
χ322222-2-2222222222222-22-2-2-2-2-2-22222-2-2220000000000000000-2-200000000-2-22200000000000000
χ332222-2-222-122-1-1-1-1-1-1-1-22-2-21111-1-1-1-122-2-200000000−i3−i3i3i3i3i3−i3−i311−i3−i3i3i3i3i3−i3−i3-1-11100000000000000
χ342222-2-222-122-1-1-1-1-1-1-1-22-2-21111-1-1-1-122-2-200000000i3i3−i3−i3−i3−i3i3i311i3i3−i3−i3−i3−i3i3i3-1-11100000000000000
χ352222-2-222-122-1-1-1-1-1-1-1-22-2-21111-1-1-1-1-2-22200000000−i3−i3i3i3i3i3−i3−i311i3i3−i3−i3−i3−i3i3i311-1-100000000000000
χ362222-2-222-122-1-1-1-1-1-1-1-22-2-21111-1-1-1-1-2-22200000000i3i3−i3−i3−i3−i3i3i311−i3−i3i3i3i3i3−i3−i311-1-100000000000000
χ372222-2-222-1-2-2-1-1-1-1-1-1-1-2-222111111112-22-222-2-222-2-2-1-1-1-11111-1-1-1-1-1-11111-11-1100000000000000
χ382222-2-222-1-2-2-1-1-1-1-1-1-1-2-222111111112-22-2-2-222-2-2221111-1-1-1-1-1-11111-1-1-1-1-11-1100000000000000
χ392222-2-222-1-2-2-1-1-1-1-1-1-1-2-22211111111-22-2222-2-2-2-2221111-1-1-1-1-1-1-1-1-1-111111-11-100000000000000
χ402222-2-222-1-2-2-1-1-1-1-1-1-1-2-22211111111-22-22-2-22222-2-2-1-1-1-11111-1-11111-1-1-1-11-11-100000000000000
χ412222-2-2-2-22222-2-2-2-2222-2-22-2-22222-2-200000000000000000000-22000000000000002200-2-2000000
χ422222-2-2-2-22222-2-2-2-2222-2-22-2-22222-2-200000000000000000000-2200000000000000-2-20022000000
χ432222-2-2-2-22-2-22-2-2-2-222222-2-2-222-2-222000000000000000000002-20000000000002-200-2200000000
χ442222-2-2-2-22-2-22-2-2-2-222222-2-2-222-2-222000000000000000000002-2000000000000-22002-200000000
χ45444444-4-4-244-22222-2-2-4-44-4-2-222-2-22200000000000000000000-2200000000000000000000000000
χ46444444-4-4-2-4-4-22222-2-2-44-44-2-22222-2-2000000000000000000002-200000000000000000000000000
χ474444-4-4-4-4-244-22222-2-24-4-4422-2-2-2-222000000000000000000002-200000000000000000000000000
χ484444-4-4-4-4-2-4-4-22222-2-2444-422-2-222-2-200000000000000000000-2200000000000000000000000000
χ4944-4-4000044-4-400004-4000000004-40000002i−2i2i−2i000000000000002i−2i2i−2i2i−2i2i−2i000000000000000000
χ5044-4-4000044-4-400004-4000000004-4000000−2i2i−2i2i00000000000000−2i2i−2i2i−2i2i−2i2i000000000000000000
χ5144-4-400004-44-400004-400000000-440000002i−2i−2i2i000000000000002i−2i2i−2i−2i2i−2i2i000000000000000000
χ5244-4-400004-44-400004-400000000-44000000−2i2i2i−2i00000000000000−2i2i−2i2i2i−2i2i−2i000000000000000000
χ5344-4-40000-24-42−2i3−2i32i32i3-2200000000-22−2i32i300002i−2i2i−2i000000000000002ζ22−2ζ222ζ14−2ζ142ζ14−2ζ142ζ22−2ζ22000000000000000000
χ5444-4-40000-24-42−2i3−2i32i32i3-2200000000-22−2i32i30000−2i2i−2i2i00000000000000−2ζ222ζ22−2ζ142ζ14−2ζ142ζ14−2ζ222ζ22000000000000000000
χ5544-4-40000-24-422i32i3−2i3−2i3-2200000000-222i3−2i300002i−2i2i−2i000000000000002ζ14−2ζ142ζ22−2ζ222ζ22−2ζ222ζ14−2ζ14000000000000000000
χ5644-4-40000-24-422i32i3−2i3−2i3-2200000000-222i3−2i30000−2i2i−2i2i00000000000000−2ζ142ζ14−2ζ222ζ22−2ζ222ζ22−2ζ142ζ14000000000000000000
χ5744-4-40000-2-442−2i3−2i32i32i3-22000000002-22i3−2i300002i−2i−2i2i000000000000002ζ22−2ζ222ζ14−2ζ14−2ζ142ζ14−2ζ222ζ22000000000000000000
χ5844-4-40000-2-442−2i3−2i32i32i3-22000000002-22i3−2i30000−2i2i2i−2i00000000000000−2ζ222ζ22−2ζ142ζ142ζ14−2ζ142ζ22−2ζ22000000000000000000
χ5944-4-40000-2-4422i32i3−2i3−2i3-22000000002-2−2i32i300002i−2i−2i2i000000000000002ζ14−2ζ142ζ22−2ζ22−2ζ222ζ22−2ζ142ζ14000000000000000000
χ6044-4-40000-2-4422i32i3−2i3−2i3-22000000002-2−2i32i30000−2i2i2i−2i00000000000000−2ζ142ζ14−2ζ222ζ222ζ22−2ζ222ζ14−2ζ14000000000000000000
χ614-44-4004-440044-44-4-4-400000000000000000000000000000000000000000000000000000000−2i22i200
χ624-44-4004-440044-44-4-4-4000000000000000000000000000000000000000000000000000000002i2−2i200
χ634-44-400-444004-44-44-4-4000000000000000000000000000000000000000000000000000000−2i22i20000
χ644-44-400-444004-44-44-4-40000000000000000000000000000000000000000000000000000002i2−2i20000
χ654-4-444-400400-40000-4400004-4000000000000002-22-22-22-22-22-20000000000000000000000000000
χ664-4-444-400400-40000-4400004-400000000000000-22-22-22-22-22-220000000000000000000000000000
χ674-4-444-400-2002−2i32i32i3−2i32-20000-22−2i32i30000000000002-22-2−1+i31−i3−1−i31+i3−1+i31−i3−1−i31+i30000000000000000000000000000
χ684-4-444-400-2002−2i32i32i3−2i32-20000-22−2i32i3000000000000-22-221−i3−1+i31+i3−1−i31−i3−1+i31+i3−1−i30000000000000000000000000000
χ694-4-444-400-20022i3−2i3−2i32i32-20000-222i3−2i30000000000002-22-2−1−i31+i3−1+i31−i3−1−i31+i3−1+i31−i30000000000000000000000000000
χ704-4-444-400-20022i3−2i3−2i32i32-20000-222i3−2i3000000000000-22-221+i3−1−i31−i3−1+i31+i3−1−i31−i3−1+i30000000000000000000000000000
χ714-4-44-4400400-40000-440000-44000000000000002-2-222-22-2-22-220000000000000000000000000000
χ724-4-44-4400400-40000-440000-4400000000000000-222-2-22-222-22-20000000000000000000000000000
χ734-4-44-4400-2002−2i32i32i3−2i32-200002-22i3−2i30000000000002-2-22−1+i31−i3−1−i31+i31−i3−1+i31+i3−1−i30000000000000000000000000000
χ744-4-44-4400-2002−2i32i32i3−2i32-200002-22i3−2i3000000000000-222-21−i3−1+i31+i3−1−i3−1+i31−i3−1−i31+i30000000000000000000000000000
χ754-4-44-4400-20022i3−2i3−2i32i32-200002-2−2i32i30000000000002-2-22−1−i31+i3−1+i31−i31+i3−1−i31−i3−1+i30000000000000000000000000000
χ764-4-44-4400-20022i3−2i3−2i32i32-200002-2−2i32i3000000000000-222-21+i3−1−i31−i3−1+i3−1−i31+i3−1+i31−i30000000000000000000000000000
χ778-88-8008-8-400-4-44-4444000000000000000000000000000000000000000000000000000000000000
χ788-88-800-88-400-44-44-444000000000000000000000000000000000000000000000000000000000000

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