Finite Group Databasebeta

← Group #11798609

Character table — Group #11798609

Order 1152.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72
size112222222444444444444448888888888888888812121212121212121212121216161616162424242424244848484848487272144
order12233666622344466661212121246666661212121212121212121244441212121212121212612121212246612124812122424244
χ1111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111-1-1-1-1-1-1111111-1-1-1
χ41111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-1111
χ5111111111111-1-111111-1-1-1-1-1111111-1-1-1-11-1-1-1-1111-1-1-1-1-1-111111-1-1-11-11-1-1111-111-1-111-1
χ6111111111111-1-111111-1-1-1-1-1111111-1-1-1-11-1-1-1-1111-1-1-1-1-1-111111-1-1-11-11-1-111-11-1-111-1-11
χ7111111111111-1-111111-1-1-1-1-1111111-1-1-1-11-1-1-1-11-1-1111111-1-1-1-11-1-1-111-111-1-11-111-1-1-1-11
χ8111111111111-1-111111-1-1-1-1-1111111-1-1-1-11-1-1-1-11-1-1111111-1-1-1-11-1-1-111-111-1-1-11-1-11111-1
χ92222222222-2200-2222200000-22-2-2-220000-20000-22200000022222000-20-200-2-2000000000
χ102222222222-2200-2222200000-22-2-2-220000-20000-2-2-2000000-2-2-2-22000-2020022000000000
χ11222222222-22222-222222222-22-2222-222-2-2-22222-2000000000000-2-2-2-2-2000000000000000
χ12222222222-222-2-2-22222-2-2-2-222-2222-2-2-222-2-2-2-2-2-2000000000000-2222-2000000000000000
χ13222222222-2-22002222200000-2-2-2-2-2-20000200002002222220000-20002-20-2-200000000000
χ14222222222-2-22002222200000-2-2-2-2-2-2000020000200-2-2-2-2-2-20000-20002202200000000000
χ152222-12-1-1-122-12222-1-1-1-1-1-1-122-1-1-1-1222-1-1-1-1-1-1-122222-1-1-1-1-1-1-1-1-12-1-1-122-1-1-1-1000000000
χ162222-12-1-1-122-12222-1-1-1-1-1-1-122-1-1-1-1222-1-1-1-1-1-1-12-2-2-2-211111111-12-1-1-1-2-21111000000000
χ172222-12-1-1-122-1-2-222-1-1-11111-22-1-1-1-12-2-211-11111222-2-21111-1-1-1-1-1-211-1-2211-1-1000000000
χ182222-12-1-1-122-1-2-222-1-1-11111-22-1-1-1-12-2-211-111112-2-222-1-1-1-11111-1-211-12-2-1-111000000000
χ192222-12-1-1-12-2-100-22-1-1-1−i3−i3i3i30-2-1111200−i3i31−i3−i3i3i3-22200−i3−i3i3i3-1-1-1-1-10−i3i310-2−i3i311000000000
χ202222-12-1-1-12-2-100-22-1-1-1−i3−i3i3i30-2-1111200−i3i31−i3−i3i3i3-2-2-200i3i3−i3−i31111-10−i3i3102i3−i3-1-1000000000
χ212222-12-1-1-12-2-100-22-1-1-1i3i3−i3−i30-2-1111200i3−i31i3i3−i3−i3-22200i3i3−i3−i3-1-1-1-1-10i3−i310-2i3−i311000000000
χ222222-12-1-1-12-2-100-22-1-1-1i3i3−i3−i30-2-1111200i3−i31i3i3−i3−i3-2-2-200−i3−i3i3i31111-10i3−i3102−i3i3-1-1000000000
χ232222-12-1-1-1-22-122-22-1-1-1-1-1-1-1-221-1-1-1-222111-1-1-1-1-20000−i3−i3i3i3−i3−i3i3i31-211100i3−i3−i3i3000000000
χ242222-12-1-1-1-22-122-22-1-1-1-1-1-1-1-221-1-1-1-222111-1-1-1-1-20000i3i3−i3−i3i3i3−i3−i31-211100−i3i3i3−i3000000000
χ252222-12-1-1-1-22-1-2-2-22-1-1-11111221-1-1-1-2-2-2-1-111111-20000−i3−i3i3i3i3i3−i3−i312-1-1100i3−i3i3−i3000000000
χ262222-12-1-1-1-22-1-2-2-22-1-1-11111221-1-1-1-2-2-2-1-111111-20000i3i3−i3−i3−i3−i3i3i312-1-1100−i3i3−i3i3000000000
χ272222-12-1-1-1-2-2-10022-1-1-1−i3−i3i3i30-21111-200i3−i3-1−i3−i3i3i320022-1-1-1-1−i3−i3i3i310i3−i3-1-2011i3−i3000000000
χ282222-12-1-1-1-2-2-10022-1-1-1−i3−i3i3i30-21111-200i3−i3-1−i3−i3i3i3200-2-21111i3i3−i3−i310i3−i3-120-1-1−i3i3000000000
χ292222-12-1-1-1-2-2-10022-1-1-1i3i3−i3−i30-21111-200−i3i3-1i3i3−i3−i320022-1-1-1-1i3i3−i3−i310−i3i3-1-2011−i3i3000000000
χ302222-12-1-1-1-2-2-10022-1-1-1i3i3−i3−i30-21111-200−i3i3-1i3i3−i3−i3200-2-21111−i3−i3i3i310−i3i3-120-1-1i3−i3000000000
χ31222-12-122222-1222-1-1-1-122222-122-1-1-1-1-1222-1-1-1-1-1000000000000-1-1-1-1-100000022-1-1-1-1000
χ32222-12-122222-1222-1-1-1-122222-122-1-1-1-1-1222-1-1-1-1-1000000000000-1-1-1-1-1000000-2-21111000
χ33222-12-122222-1-2-22-1-1-1-1-2-2-2-2-2-122-1-1-111-2-221111-1000000000000-1111-10000002-2-1-111000
χ34222-12-122222-1-2-22-1-1-1-1-2-2-2-2-2-122-1-1-111-2-221111-1000000000000-1111-1000000-2211-1-1000
χ35222-12-1222-22-122-2-1-1-1-12222-2-1-22-1-11-1-1-2-2-2-1-1-1-1100000000000011111000000003−33−3000
χ36222-12-1222-22-122-2-1-1-1-12222-2-1-22-1-11-1-1-2-2-2-1-1-1-110000000000001111100000000−33−33000
χ37222-12-1222-22-1-2-2-2-1-1-1-1-2-2-2-22-1-22-1-111122-2111110000000000001-1-1-11000000003−3−33000
χ38222-12-1222-22-1-2-2-2-1-1-1-1-2-2-2-22-1-22-1-111122-2111110000000000001-1-1-1100000000−333−3000
χ39444-24-24444-4-200-4-2-2-2-20000024-422-20000-400002000000000000-20002000000000000000
χ40444-24-2444-4-4-2004-2-2-2-2000002-4-4222000040000-20000000000002000-2000000000000000
χ41444-2-2-2-2-2-2441444-2111-2-2-2-24-2-2-211-2-2-2-2-2-21111-20000000000001-2111000000000000000
χ42444-2-2-2-2-2-2441-4-44-21112222-4-2-2-211-22222-2-1-1-1-1-200000000000012-1-11000000000000000
χ43444-2-2-2-2-2-24-4100-4-2111−2i3−2i32i32i302-22-1-1-200−2i32i32i3i3−i3−i3200000000000010i3−i3-1000000000000000
χ44444-2-2-2-2-2-24-4100-4-21112i32i3−2i3−2i302-22-1-1-2002i3−2i32−i3−i3i3i3200000000000010−i3i3-1000000000000000
χ45444-2-2-2-2-2-2-44144-4-2111-2-2-2-2-4-22-2112-2-222211112000000000000-12-1-1-1000000000000000
χ46444-2-2-2-2-2-2-441-4-4-4-211122224-22-211222-2-22-1-1-1-12000000000000-1-211-1000000000000000
χ47444-2-2-2-2-2-2-4-41004-2111−2i3−2i32i32i30222-1-12002i3−2i3-2i3i3−i3−i3-2000000000000-10−i3i31000000000000000
χ48444-2-2-2-2-2-2-4-41004-21112i32i3−2i3−2i30222-1-1200−2i32i3-2−i3−i3i3i3-2000000000000-10i3−i31000000000000000
χ4944-4444-4-44004000-4-4-44000000000000000000000000000000000000000000000000002-20
χ5044-4444-4-44004000-4-4-4400000000000000000000000000000000000000000000000000-220
χ514-4044-400-40042i−2i0000-42i−2i2i−2i00000002i−2i0002i−2i2i−2i02i−2i2-22-22-22i−2i2i−2i00000000000000000000
χ524-4044-400-40042i−2i0000-42i−2i2i−2i00000002i−2i0002i−2i2i−2i0−2i2i-22-22-22−2i2i−2i2i00000000000000000000
χ534-4044-400-4004−2i2i0000-4−2i2i−2i2i0000000−2i2i000−2i2i−2i2i02i−2i-22-22-222i−2i2i−2i00000000000000000000
χ544-4044-400-4004−2i2i0000-4−2i2i−2i2i0000000−2i2i000−2i2i−2i2i0−2i2i2-22-22-2−2i2i−2i2i00000000000000000000
χ554-404-2-4−2i32i3200-22i−2i00−2i32i322ζ7−2ζ72ζ11−2ζ1100000002i−2i0002ζ7−2ζ72ζ11−2ζ1102i−2i2-2−1+i31−i3−1−i31+i32ζ7−2ζ72ζ11−2ζ1100000000000000000000
χ564-404-2-4−2i32i3200-22i−2i00−2i32i322ζ7−2ζ72ζ11−2ζ1100000002i−2i0002ζ7−2ζ72ζ11−2ζ110−2i2i-221−i3−1+i31+i3−1−i3−2ζ72ζ7−2ζ112ζ1100000000000000000000
χ574-404-2-4−2i32i3200-2−2i2i00−2i32i32−2ζ72ζ7−2ζ112ζ110000000−2i2i000−2ζ72ζ7−2ζ112ζ1102i−2i-221−i3−1+i31+i3−1−i32ζ7−2ζ72ζ11−2ζ1100000000000000000000
χ584-404-2-4−2i32i3200-2−2i2i00−2i32i32−2ζ72ζ7−2ζ112ζ110000000−2i2i000−2ζ72ζ7−2ζ112ζ110−2i2i2-2−1+i31−i3−1−i31+i3−2ζ72ζ7−2ζ112ζ1100000000000000000000
χ594-404-2-42i3−2i3200-22i−2i002i3−2i322ζ11−2ζ112ζ7−2ζ700000002i−2i0002ζ11−2ζ112ζ7−2ζ702i−2i2-2−1−i31+i3−1+i31−i32ζ11−2ζ112ζ7−2ζ700000000000000000000
χ604-404-2-42i3−2i3200-22i−2i002i3−2i322ζ11−2ζ112ζ7−2ζ700000002i−2i0002ζ11−2ζ112ζ7−2ζ70−2i2i-221+i3−1−i31−i3−1+i3−2ζ112ζ11−2ζ72ζ700000000000000000000
χ614-404-2-42i3−2i3200-2−2i2i002i3−2i32−2ζ112ζ11−2ζ72ζ70000000−2i2i000−2ζ112ζ11−2ζ72ζ702i−2i-221+i3−1−i31−i3−1+i32ζ11−2ζ112ζ7−2ζ700000000000000000000
χ624-404-2-42i3−2i3200-2−2i2i002i3−2i32−2ζ112ζ11−2ζ72ζ70000000−2i2i000−2ζ112ζ11−2ζ72ζ70−2i2i2-2−1−i31+i3−1+i31−i3−2ζ112ζ11−2ζ72ζ700000000000000000000
χ6388-88-4844-400-4000-844-400000000000000000000000000000000000000000000000000000
χ6488-8-48-4-8-8800-4000444-400000000000000000000000000000000000000000000000000000
χ6588-8-4-4-444-40020004-2-22000000006-60000000000000000000000000000000000000000000
χ6688-8-4-4-444-40020004-2-2200000000-660000000000000000000000000000000000000000000
χ678-80-48400-800-44i−4i000044i−4i4i−4i0000000−2i2i000−2i2i−2i2i000000000000000000000000000000000
χ688-80-48400-800-4−4i4i00004−4i4i−4i4i00000002i−2i0002i−2i2i−2i000000000000000000000000000000000
χ698-80-4-44−4i34i340024i−4i002i3−2i3-24ζ7−4ζ74ζ11−4ζ110000000−2i2i000−2ζ72ζ7−2ζ112ζ11000000000000000000000000000000000
χ708-80-4-44−4i34i34002−4i4i002i3−2i3-2−4ζ74ζ7−4ζ114ζ1100000002i−2i0002ζ7−2ζ72ζ11−2ζ11000000000000000000000000000000000
χ718-80-4-444i3−4i340024i−4i00−2i32i3-24ζ11−4ζ114ζ7−4ζ70000000−2i2i000−2ζ112ζ11−2ζ72ζ7000000000000000000000000000000000
χ728-80-4-444i3−4i34002−4i4i00−2i32i3-2−4ζ114ζ11−4ζ74ζ700000002i−2i0002ζ11−2ζ112ζ7−2ζ7000000000000000000000000000000000

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