Finite Group Databasebeta

← Group #10695987

Character table — Group #10695987

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72
size1111222222222222224444444444448888888888888888888888888816161616161624242424484848484848
order1222223444466666664444121212121212121244444444121212121212121212121212121212121212246612128888248888
χ1111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-11111-1-111-1-1
χ41111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-111-1-111
χ5111111111111111111111111111111-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1
χ6111111111111111111111111111111-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ7111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11111111111-1-1-1-111
χ8111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-1
χ9222222222-2-222222222-2-2-22222-2-2-2-20000000000000000-2-2000000002-222-2-20000000000
χ10222222222-2-222222222-2-2-22222-2-2-2-20000000000000000-2-200000000-22-2-2220000000000
χ112222222-2-2222222222-2-22-2-2-2-2-22222000022-2-22222-2-2-2-2-2-2000000000000000000000000
χ122222222-2-2222222222-2-22-2-2-2-2-222220000-2-222-2-2-2-22222-2-2000000000000000000000000
χ132222222-2-2-2-22222222-22-22-2-2-2-2-2-2-2-222-2-2000000000000222222-2-2-2-20000000000000000
χ142222222-2-2-2-22222222-22-22-2-2-2-2-2-2-2-2-2-22200000000000022-2-2-2-222220000000000000000
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
χ16222222-12222-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-12222-2-2-2-211111111-1-1-1-1-1-1-1-1-1-1-2-211110000000000
χ17222222-12222-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-2-2-2-22222-1-1-1-1-1-1-1-1-1-111111111-2-211110000000000
χ18222222-12222-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-211111111-1-11111111122-1-1-1-10000000000
χ19222222-122-2-2-1-1-1-1-1-1-12-2-2-2-1-1-1-1111100000000−i3−i3i3i3−i3−i3i3i311−i3−i3i3i3−i3−i3i3i32-2-1-1110000000000
χ20222222-122-2-2-1-1-1-1-1-1-12-2-2-2-1-1-1-1111100000000−i3−i3i3i3−i3−i3i3i311i3i3−i3−i3i3i3−i3−i3-2211-1-10000000000
χ21222222-122-2-2-1-1-1-1-1-1-12-2-2-2-1-1-1-1111100000000i3i3−i3−i3i3i3−i3−i311−i3−i3i3i3−i3−i3i3i3-2211-1-10000000000
χ22222222-122-2-2-1-1-1-1-1-1-12-2-2-2-1-1-1-1111100000000i3i3−i3−i3i3i3−i3−i311i3i3−i3−i3i3i3−i3−i32-2-1-1110000000000
χ23222222-1-2-222-1-1-1-1-1-1-1-2-22-21111-1-1-1-1000022-2-2-1-1-1-1111111−i3−i3i3i3i3i3−i3−i300−i3i3−i3i30000000000
χ24222222-1-2-222-1-1-1-1-1-1-1-2-22-21111-1-1-1-1000022-2-2-1-1-1-1111111i3i3−i3−i3−i3−i3i3i300i3−i3i3−i30000000000
χ25222222-1-2-222-1-1-1-1-1-1-1-2-22-21111-1-1-1-10000-2-2221111-1-1-1-111−i3−i3i3i3i3i3−i3−i300i3−i3i3−i30000000000
χ26222222-1-2-222-1-1-1-1-1-1-1-2-22-21111-1-1-1-10000-2-2221111-1-1-1-111i3i3−i3−i3−i3−i3i3i300−i3i3−i3i30000000000
χ27222222-1-2-2-2-2-1-1-1-1-1-1-1-22-221111111122-2-20000−i3−i3i3i3i3i3−i3−i3-1-1-1-1-1-1111100−i3i3i3−i30000000000
χ28222222-1-2-2-2-2-1-1-1-1-1-1-1-22-221111111122-2-20000i3i3−i3−i3−i3−i3i3i3-1-1-1-1-1-1111100i3−i3−i3i30000000000
χ29222222-1-2-2-2-2-1-1-1-1-1-1-1-22-2211111111-2-2220000−i3−i3i3i3i3i3−i3−i3-1-11111-1-1-1-100i3−i3−i3i30000000000
χ30222222-1-2-2-2-2-1-1-1-1-1-1-1-22-2211111111-2-2220000i3i3−i3−i3−i3−i3i3i3-1-11111-1-1-1-100−i3i3i3−i30000000000
χ312222-2-222222-2-2-2-2222-22-2-222-2-222-2-200000000000000002-2000000000000000000002-200
χ322222-2-222222-2-2-2-2222-22-2-222-2-222-2-200000000000000002-200000000000000000000-2200
χ332222-2-2222-2-2-2-2-2-2222-2-22222-2-2-2-2220000000000000000-220000000000000000002-20000
χ342222-2-2222-2-2-2-2-2-2222-2-22222-2-2-2-2220000000000000000-22000000000000000000-220000
χ352222-2-22-2-222-2-2-2-22222-2-22-2-22222-2-20000000000000000-2200000000000000000000002-2
χ362222-2-22-2-222-2-2-2-22222-2-22-2-22222-2-20000000000000000-220000000000000000000000-22
χ372222-2-22-2-2-2-2-2-2-2-2222222-2-2-222-2-22200000000000000002-2000000000000002i2i−2i−2i000000
χ382222-2-22-2-2-2-2-2-2-2-2222222-2-2-222-2-22200000000000000002-200000000000000−2i−2i2i2i000000
χ394444-4-4-244442222-2-2-2-44-4-4-2-222-2-2220000000000000000-22000000000000000000000000
χ404444-4-4-244-4-42222-2-2-2-4-444-2-22222-2-200000000000000002-2000000000000000000000000
χ414444-4-4-2-4-4442222-2-2-24-4-4422-2-2-2-22200000000000000002-2000000000000000000000000
χ424444-4-4-2-4-4-4-42222-2-2-2444-422-2-222-2-20000000000000000-22000000000000000000000000
χ4344-4-4004004i−4i00004-4-4000000004i−4i002-22i−2i000000000000002-22-22i−2i2i−2i0000000000000000
χ4444-4-4004004i−4i00004-4-4000000004i−4i00-22−2i2i00000000000000-22-22−2i2i−2i2i0000000000000000
χ4544-4-400400−4i4i00004-4-400000000−4i4i002-2−2i2i000000000000002-22-2−2i2i−2i2i0000000000000000
χ4644-4-400400−4i4i00004-4-400000000−4i4i00-222i−2i00000000000000-22-222i−2i2i−2i0000000000000000
χ4744-4-400-2004i−4i−2i32i3−2i32i3-22200000000−2i2i23−232-22i−2i00000000000000−1+i31−i3−1−i31+i32ζ11−2ζ112ζ7−2ζ70000000000000000
χ4844-4-400-2004i−4i−2i32i3−2i32i3-22200000000−2i2i23−23-22−2i2i000000000000001−i3−1+i31+i3−1−i3−2ζ112ζ11−2ζ72ζ70000000000000000
χ4944-4-400-2004i−4i2i3−2i32i3−2i3-22200000000−2i2i−23232-22i−2i00000000000000−1−i31+i3−1+i31−i32ζ7−2ζ72ζ11−2ζ110000000000000000
χ5044-4-400-2004i−4i2i3−2i32i3−2i3-22200000000−2i2i−2323-22−2i2i000000000000001+i3−1−i31−i3−1+i3−2ζ72ζ7−2ζ112ζ110000000000000000
χ5144-4-400-200−4i4i−2i32i3−2i32i3-222000000002i−2i−23232-2−2i2i00000000000000−1+i31−i3−1−i31+i3−2ζ112ζ11−2ζ72ζ70000000000000000
χ5244-4-400-200−4i4i−2i32i3−2i32i3-222000000002i−2i−2323-222i−2i000000000000001−i3−1+i31+i3−1−i32ζ11−2ζ112ζ7−2ζ70000000000000000
χ5344-4-400-200−4i4i2i3−2i32i3−2i3-222000000002i−2i23−232-2−2i2i00000000000000−1−i31+i3−1+i31−i3−2ζ72ζ7−2ζ112ζ110000000000000000
χ5444-4-400-200−4i4i2i3−2i32i3−2i3-222000000002i−2i23−23-222i−2i000000000000001+i3−1−i31−i3−1+i32ζ7−2ζ72ζ11−2ζ110000000000000000
χ554-44-40044-4000000-44-400004-400000000002i−2i2i−2i2i−2i2i−2i2i−2i2i−2i00000000000000000000000000
χ564-44-40044-4000000-44-400004-40000000000−2i2i−2i2i−2i2i−2i2i−2i2i−2i2i00000000000000000000000000
χ574-44-4004-44000000-44-40000-4400000000002i−2i−2i2i2i−2i2i−2i−2i2i−2i2i00000000000000000000000000
χ584-44-4004-44000000-44-40000-440000000000−2i2i2i−2i−2i2i−2i2i2i−2i2i−2i00000000000000000000000000
χ594-44-400-24-400−2i32i32i3−2i32-220000-22−2i32i3000000002i−2i2i−2i2ζ7−2ζ72ζ11−2ζ112ζ7−2ζ72ζ11−2ζ1100000000000000000000000000
χ604-44-400-24-400−2i32i32i3−2i32-220000-22−2i32i300000000−2i2i−2i2i−2ζ72ζ7−2ζ112ζ11−2ζ72ζ7−2ζ112ζ1100000000000000000000000000
χ614-44-400-24-4002i3−2i3−2i32i32-220000-222i3−2i3000000002i−2i2i−2i2ζ11−2ζ112ζ7−2ζ72ζ11−2ζ112ζ7−2ζ700000000000000000000000000
χ624-44-400-24-4002i3−2i3−2i32i32-220000-222i3−2i300000000−2i2i−2i2i−2ζ112ζ11−2ζ72ζ7−2ζ112ζ11−2ζ72ζ700000000000000000000000000
χ634-44-400-2-4400−2i32i32i3−2i32-2200002-22i3−2i3000000002i−2i−2i2i2ζ7−2ζ72ζ11−2ζ11−2ζ72ζ7−2ζ112ζ1100000000000000000000000000
χ644-44-400-2-4400−2i32i32i3−2i32-2200002-22i3−2i300000000−2i2i2i−2i−2ζ72ζ7−2ζ112ζ112ζ7−2ζ72ζ11−2ζ1100000000000000000000000000
χ654-44-400-2-44002i3−2i3−2i32i32-2200002-2−2i32i3000000002i−2i−2i2i2ζ11−2ζ112ζ7−2ζ7−2ζ112ζ11−2ζ72ζ700000000000000000000000000
χ664-44-400-2-44002i3−2i3−2i32i32-2200002-2−2i32i300000000−2i2i2i−2i−2ζ112ζ11−2ζ72ζ72ζ11−2ζ112ζ7−2ζ700000000000000000000000000
χ674-4-444-44000044-4-4-4-44000000000000000000000000000000000000000000002i−2i2i−2i000000
χ684-4-444-44000044-4-4-4-4400000000000000000000000000000000000000000000−2i2i−2i2i000000
χ694-4-44-4440000-4-444-4-44000000000000000000000000000000000000000000002-2-22000000
χ704-4-44-4440000-4-444-4-4400000000000000000000000000000000000000000000-222-2000000
χ718-8-888-8-40000-4-44444-4000000000000000000000000000000000000000000000000000000
χ728-8-88-88-4000044-4-444-4000000000000000000000000000000000000000000000000000000

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