Finite Group Databasebeta

← Group #10696001

Character table — Group #10696001

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72
size1111222222222222224444444444448888888888888888888888888816161616161624242424484848484848
order122222344446666666444412121212121212122244444466661212121212121212121212121212246612128888448888
χ1111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111-1-111-1-1
χ41111111111111111111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-111-1-111
χ5111111111111111111111111111111-1-1-1-11111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1
χ6111111111111111111111111111111-1-1-1-11111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ7111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-111
χ8111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-1
χ9222222222-2-222222222-2-2-22222-2-2-2-2000022-2-20000-2-22222-2-2-2-200000000000000000000
χ10222222222-2-222222222-2-2-22222-2-2-2-20000-2-2220000-2-2-2-2-2-2222200000000000000000000
χ112222222-2-2222222222-2-22-2-2-2-2-22222000000000000-2-20000000000002-222-2-20000000000
χ122222222-2-2222222222-2-22-2-2-2-2-22222000000000000-2-2000000000000-22-2-2220000000000
χ132222222-2-2-2-22222222-22-22-2-2-2-2-2-2-2-222-2-2000022222200000000-2-2-2-20000000000000000
χ142222222-2-2-2-22222222-22-22-2-2-2-2-2-2-2-2-2-2220000-2-2-2-2220000000022220000000000000000
χ15222222-12222-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122-1-1-1-10000000000
χ16222222-12222-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-12222-2-2-2-2-1-1-1-1-1-111111111-1-1-1-1-2-211110000000000
χ17222222-12222-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-2-2-2-222221111-1-1-1-1-1-1-1-1-1-11111-2-211110000000000
χ18222222-12222-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-21111-1-111111111111122-1-1-1-10000000000
χ19222222-122-2-2-1-1-1-1-1-1-12-2-2-2-1-1-1-11111000022-2-2−i3−i3i3i311-1-1-1-11111−i3−i3i3i300−i3i3−i3i30000000000
χ20222222-122-2-2-1-1-1-1-1-1-12-2-2-2-1-1-1-11111000022-2-2i3i3−i3−i311-1-1-1-11111i3i3−i3−i300i3−i3i3−i30000000000
χ21222222-122-2-2-1-1-1-1-1-1-12-2-2-2-1-1-1-111110000-2-222−i3−i3i3i3111111-1-1-1-1−i3−i3i3i300i3−i3i3−i30000000000
χ22222222-122-2-2-1-1-1-1-1-1-12-2-2-2-1-1-1-111110000-2-222i3i3−i3−i3111111-1-1-1-1i3i3−i3−i300−i3i3−i3i30000000000
χ23222222-1-2-222-1-1-1-1-1-1-1-2-22-21111-1-1-1-100000000−i3−i3i3i311−i3−i3i3i3−i3−i3i3i3i3i3−i3−i32-2-1-1110000000000
χ24222222-1-2-222-1-1-1-1-1-1-1-2-22-21111-1-1-1-100000000−i3−i3i3i311i3i3−i3−i3i3i3−i3−i3i3i3−i3−i3-2211-1-10000000000
χ25222222-1-2-222-1-1-1-1-1-1-1-2-22-21111-1-1-1-100000000i3i3−i3−i311−i3−i3i3i3−i3−i3i3i3−i3−i3i3i3-2211-1-10000000000
χ26222222-1-2-222-1-1-1-1-1-1-1-2-22-21111-1-1-1-100000000i3i3−i3−i311i3i3−i3−i3i3i3−i3−i3−i3−i3i3i32-2-1-1110000000000
χ27222222-1-2-2-2-2-1-1-1-1-1-1-1-22-221111111122-2-20000-1-1-1-1-1-1−i3−i3i3i3i3i3−i3−i3111100−i3i3i3−i30000000000
χ28222222-1-2-2-2-2-1-1-1-1-1-1-1-22-221111111122-2-20000-1-1-1-1-1-1i3i3−i3−i3−i3−i3i3i3111100i3−i3−i3i30000000000
χ29222222-1-2-2-2-2-1-1-1-1-1-1-1-22-2211111111-2-22200001111-1-1−i3−i3i3i3i3i3−i3−i3-1-1-1-100i3−i3−i3i30000000000
χ30222222-1-2-2-2-2-1-1-1-1-1-1-1-22-2211111111-2-22200001111-1-1i3i3−i3−i3−i3−i3i3i3-1-1-1-100−i3i3i3−i30000000000
χ312222-2-222222-2-222-2-22-22-2-222-2-222-2-20000000000002-20000000000000000000000002-200
χ322222-2-222222-2-222-2-22-22-2-222-2-222-2-20000000000002-2000000000000000000000000-2200
χ332222-2-2222-2-2-2-222-2-22-2-22222-2-2-2-222000000000000-22000000000000000000000000002-2
χ342222-2-2222-2-2-2-222-2-22-2-22222-2-2-2-222000000000000-2200000000000000000000000000-22
χ352222-2-22-2-222-2-222-2-222-2-22-2-22222-2-2000000000000-2200000000000000000000002-20000
χ362222-2-22-2-222-2-222-2-222-2-22-2-22222-2-2000000000000-220000000000000000000000-220000
χ372222-2-22-2-2-2-2-2-222-2-22222-2-2-222-2-2220000000000002-20000000000000000002i2i−2i−2i000000
χ382222-2-22-2-2-2-2-2-222-2-22222-2-2-222-2-2220000000000002-2000000000000000000−2i−2i2i2i000000
χ394444-4-4-2444422-2-222-2-44-4-4-2-222-2-222000000000000-220000000000000000000000000000
χ404444-4-4-244-4-422-2-222-2-4-444-2-22222-2-20000000000002-20000000000000000000000000000
χ414444-4-4-2-4-44422-2-222-24-4-4422-2-2-2-2220000000000002-20000000000000000000000000000
χ424444-4-4-2-4-4-4-422-2-222-2444-422-2-222-2-2000000000000-220000000000000000000000000000
χ4344-4-44-440000444-4-4-4-4000000000000000000000000000000000000000000002-22-2000000
χ4444-4-44-440000444-4-4-4-400000000000000000000000000000000000000000000-22-22000000
χ4544-4-4-4440000-4-44-444-4000000000000000000000000000000000000000000002i−2i−2i2i000000
χ4644-4-4-4440000-4-44-444-400000000000000000000000000000000000000000000−2i2i2i−2i000000
χ474-44-40044i−4i0000-4400-400004i−4i0000002-22i−2i00002-22-200000000002i−2i2i−2i0000000000000000
χ484-44-40044i−4i0000-4400-400004i−4i000000-22−2i2i0000-22-220000000000−2i2i−2i2i0000000000000000
χ494-44-4004−4i4i0000-4400-40000−4i4i0000002-2−2i2i00002-22-20000000000−2i2i−2i2i0000000000000000
χ504-44-4004−4i4i0000-4400-40000−4i4i000000-222i−2i0000-22-2200000000002i−2i2i−2i0000000000000000
χ514-44-400-24i−4i00−2i32i32-2−2i32i320000−2i2i23−2300002-22i−2i0000−1−i31+i3−1+i31−i300000000002ζ11−2ζ112ζ7−2ζ70000000000000000
χ524-44-400-24i−4i00−2i32i32-2−2i32i320000−2i2i23−230000-22−2i2i00001+i3−1−i31−i3−1+i30000000000−2ζ112ζ11−2ζ72ζ70000000000000000
χ534-44-400-24i−4i002i3−2i32-22i3−2i320000−2i2i−232300002-22i−2i0000−1+i31−i3−1−i31+i300000000002ζ7−2ζ72ζ11−2ζ110000000000000000
χ544-44-400-24i−4i002i3−2i32-22i3−2i320000−2i2i−23230000-22−2i2i00001−i3−1+i31+i3−1−i30000000000−2ζ72ζ7−2ζ112ζ110000000000000000
χ554-44-400-2−4i4i00−2i32i32-2−2i32i3200002i−2i−232300002-2−2i2i0000−1−i31+i3−1+i31−i30000000000−2ζ112ζ11−2ζ72ζ70000000000000000
χ564-44-400-2−4i4i00−2i32i32-2−2i32i3200002i−2i−23230000-222i−2i00001+i3−1−i31−i3−1+i300000000002ζ11−2ζ112ζ7−2ζ70000000000000000
χ574-44-400-2−4i4i002i3−2i32-22i3−2i3200002i−2i23−2300002-2−2i2i0000−1+i31−i3−1−i31+i30000000000−2ζ72ζ7−2ζ112ζ110000000000000000
χ584-44-400-2−4i4i002i3−2i32-22i3−2i3200002i−2i23−230000-222i−2i00001−i3−1+i31+i3−1−i300000000002ζ7−2ζ72ζ11−2ζ110000000000000000
χ594-4-44004004-400-4-4004000000004-40000002-22-20000002-22-22-22-200000000000000000000
χ604-4-44004004-400-4-4004000000004-4000000-22-22000000-22-22-22-2200000000000000000000
χ614-4-4400400-4400-4-400400000000-440000002-2-220000002-22-2-22-2200000000000000000000
χ624-4-4400400-4400-4-400400000000-44000000-222-2000000-22-222-22-200000000000000000000
χ634-4-4400-2004-4−2i32i3222i3−2i3-200000000-22−2i32i300002-22-2000000−1+i31−i3−1−i31+i3−1+i31−i3−1−i31+i300000000000000000000
χ644-4-4400-2004-4−2i32i3222i3−2i3-200000000-22−2i32i30000-22-220000001−i3−1+i31+i3−1−i31−i3−1+i31+i3−1−i300000000000000000000
χ654-4-4400-2004-42i3−2i322−2i32i3-200000000-222i3−2i300002-22-2000000−1−i31+i3−1+i31−i3−1−i31+i3−1+i31−i300000000000000000000
χ664-4-4400-2004-42i3−2i322−2i32i3-200000000-222i3−2i30000-22-220000001+i3−1−i31−i3−1+i31+i3−1−i31−i3−1+i300000000000000000000
χ674-4-4400-200-44−2i32i3222i3−2i3-2000000002-22i3−2i300002-2-22000000−1+i31−i3−1−i31+i31−i3−1+i31+i3−1−i300000000000000000000
χ684-4-4400-200-44−2i32i3222i3−2i3-2000000002-22i3−2i30000-222-20000001−i3−1+i31+i3−1−i3−1+i31−i3−1−i31+i300000000000000000000
χ694-4-4400-200-442i3−2i322−2i32i3-2000000002-2−2i32i300002-2-22000000−1−i31+i3−1+i31−i31+i3−1−i31−i3−1+i300000000000000000000
χ704-4-4400-200-442i3−2i322−2i32i3-2000000002-2−2i32i30000-222-20000001+i3−1−i31−i3−1+i3−1−i31+i3−1+i31−i300000000000000000000
χ7188-8-88-8-40000-4-4-44444000000000000000000000000000000000000000000000000000000
χ7288-8-8-88-4000044-44-4-44000000000000000000000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 12 (ζ12 = 1); i = ζ3.