Finite Group Databasebeta

← Group #10697589

Character table — Group #10697589

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75
size111122222222222222224444444444488888888888888888888888888161616161616242424242424242448484848
order122222344444466666664441212121212121212444444441212121212121212121212121212121212124412121212888888882488
χ1111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-111111111-1-1-1-1
χ411111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ51111111111111111111111111111111-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-111
χ61111111111111111111111111111111-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1
χ71111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11111111111-1-1-1-111-1-1
χ81111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-111
χ92222222222-2-222222222-2-2-22222-2-2-2-222-2-2000000000000-2-22222-2-2-2-2000000000000000000
χ102222222222-2-222222222-2-2-22222-2-2-2-2-2-222000000000000-2-2-2-2-2-22222000000000000000000
χ112222222-2-2-222-22222222-22-2-2-2-2-222220000000000000000-2-2000000002-222-2-2000000000000
χ122222222-2-2-222-22222222-22-2-2-2-2-222220000000000000000-2-200000000-22-2-222000000000000
χ132222222-2-2-2-2-2-222222222-22-2-2-2-2-2-2-2-2000022-2-22222-2-2-2-22200000000000000000000000000
χ142222222-2-2-2-2-2-222222222-22-2-2-2-2-2-2-2-20000-2-222-2-2-2-222222200000000000000000000000000
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
χ16222222-1222222-1-1-1-1-1-1-1222-1-1-1-1-1-1-1-12222-2-2-2-211111111-1-1-1-1-1-1-1-1-1-1-2-21111000000000000
χ17222222-1222222-1-1-1-1-1-1-1222-1-1-1-1-1-1-1-1-2-2-2-22222-1-1-1-1-1-1-1-1-1-111111111-2-21111000000000000
χ18222222-1222222-1-1-1-1-1-1-1222-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-211111111-1-11111111122-1-1-1-1000000000000
χ19222222-1222-2-22-1-1-1-1-1-1-1-2-2-2-1-1-1-1111122-2-20000−i3−i3i3i3−i3−i3i3i311-1-1-1-1111100−i3i3−i3i3000000000000
χ20222222-1222-2-22-1-1-1-1-1-1-1-2-2-2-1-1-1-1111122-2-20000i3i3−i3−i3i3i3−i3−i311-1-1-1-1111100i3−i3i3−i3000000000000
χ21222222-1222-2-22-1-1-1-1-1-1-1-2-2-2-1-1-1-11111-2-2220000−i3−i3i3i3−i3−i3i3i3111111-1-1-1-100i3−i3i3−i3000000000000
χ22222222-1222-2-22-1-1-1-1-1-1-1-2-2-2-1-1-1-11111-2-2220000i3i3−i3−i3i3i3−i3−i3111111-1-1-1-100−i3i3−i3i3000000000000
χ23222222-1-2-2-222-2-1-1-1-1-1-1-1-22-21111-1-1-1-100000000−i3−i3i3i3i3i3−i3−i311−i3−i3i3i3−i3−i3i3i32-2-1-111000000000000
χ24222222-1-2-2-222-2-1-1-1-1-1-1-1-22-21111-1-1-1-100000000−i3−i3i3i3i3i3−i3−i311i3i3−i3−i3i3i3−i3−i3-2211-1-1000000000000
χ25222222-1-2-2-222-2-1-1-1-1-1-1-1-22-21111-1-1-1-100000000i3i3−i3−i3−i3−i3i3i311−i3−i3i3i3−i3−i3i3i3-2211-1-1000000000000
χ26222222-1-2-2-222-2-1-1-1-1-1-1-1-22-21111-1-1-1-100000000i3i3−i3−i3−i3−i3i3i311i3i3−i3−i3i3i3−i3−i32-2-1-111000000000000
χ27222222-1-2-2-2-2-2-2-1-1-1-1-1-1-12-2211111111000022-2-2-1-1-1-11111-1-1−i3−i3i3i3i3i3−i3−i300−i3i3i3−i3000000000000
χ28222222-1-2-2-2-2-2-2-1-1-1-1-1-1-12-2211111111000022-2-2-1-1-1-11111-1-1i3i3−i3−i3−i3−i3i3i300i3−i3−i3i3000000000000
χ29222222-1-2-2-2-2-2-2-1-1-1-1-1-1-12-22111111110000-2-2221111-1-1-1-1-1-1−i3−i3i3i3i3i3−i3−i300i3−i3−i3i3000000000000
χ30222222-1-2-2-2-2-2-2-1-1-1-1-1-1-12-22111111110000-2-2221111-1-1-1-1-1-1i3i3−i3−i3−i3−i3i3i300−i3i3i3−i3000000000000
χ312222-2-2222-222-2-2-2-2-2222-2-2222-2-222-2-200000000000000002-20000000000000022-2-200000000
χ322222-2-2222-222-2-2-2-2-2222-2-2222-2-222-2-200000000000000002-200000000000000-2-22200000000
χ332222-2-2222-2-2-2-2-2-2-2-222222-222-2-2-2-2220000000000000000-220000000000000000002i2i−2i−2i0000
χ342222-2-2222-2-2-2-2-2-2-2-222222-222-2-2-2-2220000000000000000-22000000000000000000−2i−2i2i2i0000
χ352222-2-22-2-22222-2-2-2-22222-2-2-2-22222-2-20000000000000000-2200000000000000000000002-200
χ362222-2-22-2-22222-2-2-2-22222-2-2-2-22222-2-20000000000000000-220000000000000000000000-2200
χ372222-2-22-2-22-2-22-2-2-2-2222-222-2-222-2-22200000000000000002-20000000000000000000000002-2
χ382222-2-22-2-22-2-22-2-2-2-2222-222-2-222-2-22200000000000000002-2000000000000000000000000-22
χ392-2-222-222-2-200222-2-22-2-20002-22-20000002-20000000000000000002-22-2000000−i2i2−i2i2−i2i2−i2i20000
χ402-2-222-222-2-200222-2-22-2-20002-22-20000002-20000000000000000002-22-2000000i2−i2i2−i2i2−i2i2−i20000
χ412-2-222-222-2-200222-2-22-2-20002-22-2000000-22000000000000000000-22-22000000−i2i2−i2i2i2−i2i2−i20000
χ422-2-222-222-2-200222-2-22-2-20002-22-2000000-22000000000000000000-22-22000000i2−i2i2−i2−i2i2−i2i20000
χ432-2-22-2222-2200-2-2-2222-2-20002-2-2200002i−2i00000000000000002i−2i2i−2i0000000000−i2i2i2−i22−2−220000
χ442-2-22-2222-2200-2-2-2222-2-20002-2-2200002i−2i00000000000000002i−2i2i−2i0000000000i2−i2−i2i2−222−20000
χ452-2-22-2222-2200-2-2-2222-2-20002-2-220000−2i2i0000000000000000−2i2i−2i2i0000000000−i2i2i2−i2−222−20000
χ462-2-22-2222-2200-2-2-2222-2-20002-2-220000−2i2i0000000000000000−2i2i−2i2i0000000000i2−i2−i2i22−2−220000
χ474444-4-4-244-444-42222-2-2-2-4-44-2-222-2-2220000000000000000-2200000000000000000000000000
χ484444-4-4-244-4-4-4-42222-2-2-244-4-2-22222-2-200000000000000002-200000000000000000000000000
χ494444-4-4-2-4-444442222-2-2-24-4-422-2-2-2-22200000000000000002-200000000000000000000000000
χ504444-4-4-2-4-44-4-442222-2-2-2-44422-2-222-2-20000000000000000-2200000000000000000000000000
χ514-44-40040004-400000-4-4400000004-40000002i−2i2i−2i2i−2i2i−2i2i−2i2i−2i0000000000000000000000000000
χ524-44-40040004-400000-4-4400000004-4000000−2i2i−2i2i−2i2i−2i2i−2i2i−2i2i0000000000000000000000000000
χ534-44-4004000-4400000-4-440000000-440000002i−2i−2i2i2i−2i2i−2i−2i2i−2i2i0000000000000000000000000000
χ544-44-4004000-4400000-4-440000000-44000000−2i2i2i−2i−2i2i−2i2i2i−2i2i−2i0000000000000000000000000000
χ554-44-400-20004-40−2i32i3−2i32i322-20000000-22−2i32i300002i−2i2i−2i2ζ14−2ζ142ζ22−2ζ222ζ22−2ζ222ζ14−2ζ140000000000000000000000000000
χ564-44-400-20004-40−2i32i3−2i32i322-20000000-22−2i32i30000−2i2i−2i2i−2ζ142ζ14−2ζ222ζ22−2ζ222ζ22−2ζ142ζ140000000000000000000000000000
χ574-44-400-20004-402i3−2i32i3−2i322-20000000-222i3−2i300002i−2i2i−2i2ζ22−2ζ222ζ14−2ζ142ζ14−2ζ142ζ22−2ζ220000000000000000000000000000
χ584-44-400-20004-402i3−2i32i3−2i322-20000000-222i3−2i30000−2i2i−2i2i−2ζ222ζ22−2ζ142ζ14−2ζ142ζ14−2ζ222ζ220000000000000000000000000000
χ594-44-400-2000-440−2i32i3−2i32i322-200000002-22i3−2i300002i−2i−2i2i2ζ14−2ζ142ζ22−2ζ22−2ζ222ζ22−2ζ142ζ140000000000000000000000000000
χ604-44-400-2000-440−2i32i3−2i32i322-200000002-22i3−2i30000−2i2i2i−2i−2ζ142ζ14−2ζ222ζ222ζ22−2ζ222ζ14−2ζ140000000000000000000000000000
χ614-44-400-2000-4402i3−2i32i3−2i322-200000002-2−2i32i300002i−2i−2i2i2ζ22−2ζ222ζ14−2ζ14−2ζ142ζ14−2ζ222ζ220000000000000000000000000000
χ624-44-400-2000-4402i3−2i32i3−2i322-200000002-2−2i32i30000−2i2i2i−2i−2ζ222ζ22−2ζ142ζ142ζ14−2ζ142ζ22−2ζ220000000000000000000000000000
χ634-4-444-44-44400-444-4-44-4-4000-44-44000000000000000000000000000000000000000000000000
χ644-4-444-4-24-4-4004-2-222-222000-22-220000004-4000000000000000000-22-22000000000000000000
χ654-4-444-4-24-4-4004-2-222-222000-22-22000000-440000000000000000002-22-2000000000000000000
χ664-4-444-4-2-44400-4-2-222-2220002-22-200000000000000000000000000−2i32i32i3−2i3000000000000000000
χ674-4-444-4-2-44400-4-2-222-2220002-22-2000000000000000000000000002i3−2i3−2i32i3000000000000000000
χ684-4-44-444-44-4004-4-4444-4-4000-444-4000000000000000000000000000000000000000000000000
χ694-4-44-44-24-4400-422-2-2-222000-222-200004i−4i0000000000000000−2i2i−2i2i0000000000000000000000
χ704-4-44-44-24-4400-422-2-2-222000-222-20000−4i4i00000000000000002i−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
χ7388-8-80080000000000-88-80000000000000000000000000000000000000000000000000000000
χ7488-8-800-4000000−4i34i34i3−4i34-440000000000000000000000000000000000000000000000000000000
χ7588-8-800-40000004i3−4i3−4i34i34-440000000000000000000000000000000000000000000000000000000

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