Finite Group Databasebeta

← Group #72796

Character table — Group #72796

Order 384.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69
size112222222888888888888881122222228888888888888811222222288888888888888
order12222444422444488888888366661212121266121212122424242424242424366661212121266121212122424242424242424
χ1111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111-1-111-1-1-1-1-1-11111111111111-1-111-1-1-1-1-1-11111111111111-1-111-1-1-1-1-1-1
χ311111111111-1-111-1-1-1-111-1-111111111111-1-111-1-1-1-111-1-111111111111-1-111-1-1-1-111-1-1
χ411111111111-1-1-1-1-1-111-1-11111111111111-1-1-1-1-1-111-1-11111111111111-1-1-1-1-1-111-1-111
χ5111111111-1-11111-1-1-1-1-1-111111111111-1-11111-1-1-1-1-1-111111111111-1-11111-1-1-1-1-1-111
χ6111111111-1-111-1-1-1-11111-1-1111111111-1-111-1-1-1-11111-1-1111111111-1-111-1-1-1-11111-1-1
χ7111111111-1-1-1-1111111-1-1-1-1111111111-1-1-1-1111111-1-1-1-1111111111-1-1-1-1111111-1-1-1-1
χ8111111111-1-1-1-1-1-111-1-11111111111111-1-1-1-1-1-111-1-11111111111111-1-1-1-1-1-111-1-11111
χ922222-2-2-2-2000000002i−2i000022222-2-2-2-2000000002i−2i000022222-2-2-2-2000000002i−2i0000
χ1022222-2-2-2-200000000−2i2i000022222-2-2-2-200000000−2i2i000022222-2-2-2-200000000−2i2i0000
χ11222-2-22-2-22002i−2i0000000000222-2-22-2-22002i−2i0000000000222-2-22-2-22002i−2i0000000000
χ12222-2-22-2-2200−2i2i0000000000222-2-22-2-2200−2i2i0000000000222-2-22-2-2200−2i2i0000000000
χ13222-2-2-222-200000000002i−2i00222-2-2-222-200000000002i−2i00222-2-2-222-200000000002i−2i00
χ14222-2-2-222-20000000000−2i2i00222-2-2-222-20000000000−2i2i00222-2-2-222-20000000000−2i2i00
χ1522-22-222-2-200002i−2i0000000022-22-222-2-200002i−2i0000000022-22-222-2-200002i−2i00000000
χ1622-22-222-2-20000−2i2i0000000022-22-222-2-20000−2i2i0000000022-22-222-2-20000−2i2i00000000
χ1722-22-2-2-2220000002-200000022-22-2-2-2220000002-200000022-22-2-2-2220000002-2000000
χ1822-22-2-2-222000000-2200000022-22-2-2-222000000-2200000022-22-2-2-222000000-22000000
χ1922-2-222-22-20000000000002i−2i22-2-222-22-20000000000002i−2i22-2-222-22-20000000000002i−2i
χ2022-2-222-22-2000000000000−2i2i22-2-222-22-2000000000000−2i2i22-2-222-22-2000000000000−2i2i
χ2122-2-22-22-222-200000000000022-2-22-22-222-200000000000022-2-22-22-222-2000000000000
χ2222-2-22-22-22-2200000000000022-2-22-22-22-2200000000000022-2-22-22-22-22000000000000
χ238-80000000000000000000008-80000000000000000000008-8000000000000000000000
χ2411111111111111111111111−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32
χ251111111111111-1-111-1-1-1-1-1-1−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i321−i321−i32−1+i32−1+i321−i321−i321−i321−i321−i321−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i321+i321+i32−1−i32−1−i321+i321+i321+i321+i321+i321+i32
χ2611111111111-1-111-1-1-1-111-1-1−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i321−i321−i32−1+i32−1+i321−i321−i321−i321−i32−1+i32−1+i321−i321−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i321+i321+i32−1−i32−1−i321+i321+i321+i321+i32−1−i32−1−i321+i321+i32
χ2711111111111-1-1-1-1-1-111-1-111−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−i321−i321−i32−1+i32−1+i321−i321−i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+i321+i321+i32−1−i32−1−i321+i321+i32−1−i32−1−i32
χ28111111111-1-11111-1-1-1-1-1-111−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i321−i321−i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−i321−i321−i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i321+i321+i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+i321+i321+i32−1−i32−1−i32
χ29111111111-1-111-1-1-1-11111-1-1−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i321−i321−i32−1+i32−1+i321−i321−i321−i321−i32−1+i32−1+i32−1+i32−1+i321−i321−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i321+i321+i32−1−i32−1−i321+i321+i321+i321+i32−1−i32−1−i32−1−i32−1−i321+i321+i32
χ30111111111-1-1-1-1111111-1-1-1-1−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+i32
χ31111111111-1-1-1-1-1-111-1-11111−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−i321−i321−i32−1+i32−1+i321−i321−i32−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+i321+i321+i32−1−i32−1−i321+i321+i32−1−i32−1−i32−1−i32−1−i32
χ3222222-2-2-2-2000000002i−2i0000−1+i3−1+i3−1+i3−1+i3−1+i31−i31−i31−i31−i3000000002ζ7−2ζ70000−1−i3−1−i3−1−i3−1−i3−1−i31+i31+i31+i31+i3000000002ζ11−2ζ110000
χ3322222-2-2-2-200000000−2i2i0000−1+i3−1+i3−1+i3−1+i3−1+i31−i31−i31−i31−i300000000−2ζ72ζ70000−1−i3−1−i3−1−i3−1−i3−1−i31+i31+i31+i31+i300000000−2ζ112ζ110000
χ34222-2-22-2-22002i−2i0000000000−1+i3−1+i3−1+i31−i31−i3−1+i31−i31−i3−1+i3002ζ7−2ζ70000000000−1−i3−1−i3−1−i31+i31+i3−1−i31+i31+i3−1−i3002ζ11−2ζ110000000000
χ35222-2-22-2-2200−2i2i0000000000−1+i3−1+i3−1+i31−i31−i3−1+i31−i31−i3−1+i300−2ζ72ζ70000000000−1−i3−1−i3−1−i31+i31+i3−1−i31+i31+i3−1−i300−2ζ112ζ110000000000
χ36222-2-2-222-200000000002i−2i00−1+i3−1+i3−1+i31−i31−i31−i3−1+i3−1+i31−i300000000002ζ7−2ζ700−1−i3−1−i3−1−i31+i31+i31+i3−1−i3−1−i31+i300000000002ζ11−2ζ1100
χ37222-2-2-222-20000000000−2i2i00−1+i3−1+i3−1+i31−i31−i31−i3−1+i3−1+i31−i30000000000−2ζ72ζ700−1−i3−1−i3−1−i31+i31+i31+i3−1−i3−1−i31+i30000000000−2ζ112ζ1100
χ3822-22-222-2-200002i−2i00000000−1+i3−1+i31−i3−1+i31−i3−1+i3−1+i31−i31−i300002ζ7−2ζ700000000−1−i3−1−i31+i3−1−i31+i3−1−i3−1−i31+i31+i300002ζ11−2ζ1100000000
χ3922-22-222-2-20000−2i2i00000000−1+i3−1+i31−i3−1+i31−i3−1+i3−1+i31−i31−i30000−2ζ72ζ700000000−1−i3−1−i31+i3−1−i31+i3−1−i3−1−i31+i31+i30000−2ζ112ζ1100000000
χ4022-22-2-2-2220000002-2000000−1+i3−1+i31−i3−1+i31−i31−i31−i3−1+i3−1+i3000000−1+i31−i3000000−1−i3−1−i31+i3−1−i31+i31+i31+i3−1−i3−1−i3000000−1−i31+i3000000
χ4122-22-2-2-222000000-22000000−1+i3−1+i31−i3−1+i31−i31−i31−i3−1+i3−1+i30000001−i3−1+i3000000−1−i3−1−i31+i3−1−i31+i31+i31+i3−1−i3−1−i30000001+i3−1−i3000000
χ4222-2-222-22-20000000000002i−2i−1+i3−1+i31−i31−i3−1+i3−1+i31−i3−1+i31−i30000000000002ζ7−2ζ7−1−i3−1−i31+i31+i3−1−i3−1−i31+i3−1−i31+i30000000000002ζ11−2ζ11
χ4322-2-222-22-2000000000000−2i2i−1+i3−1+i31−i31−i3−1+i3−1+i31−i3−1+i31−i3000000000000−2ζ72ζ7−1−i3−1−i31+i31+i3−1−i3−1−i31+i3−1−i31+i3000000000000−2ζ112ζ11
χ4422-2-22-22-222-2000000000000−1+i3−1+i31−i31−i3−1+i31−i3−1+i31−i3−1+i3−1+i31−i3000000000000−1−i3−1−i31+i31+i3−1−i31+i3−1−i31+i3−1−i3−1−i31+i3000000000000
χ4522-2-22-22-22-22000000000000−1+i3−1+i31−i31−i3−1+i31−i3−1+i31−i3−1+i31−i3−1+i3000000000000−1−i3−1−i31+i31+i3−1−i31+i3−1−i31+i3−1−i31+i3−1−i3000000000000
χ468-8000000000000000000000−4+4i34−4i3000000000000000000000−4−4i34+4i3000000000000000000000
χ4711111111111111111111111−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32
χ481111111111111-1-111-1-1-1-1-1-1−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i321+i321+i32−1−i32−1−i321+i321+i321+i321+i321+i321+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i321−i321−i32−1+i32−1+i321−i321−i321−i321−i321−i321−i32
χ4911111111111-1-111-1-1-1-111-1-1−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i321+i321+i32−1−i32−1−i321+i321+i321+i321+i32−1−i32−1−i321+i321+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i321−i321−i32−1+i32−1+i321−i321−i321−i321−i32−1+i32−1+i321−i321−i32
χ5011111111111-1-1-1-1-1-111-1-111−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+i321+i321+i32−1−i32−1−i321+i321+i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−i321−i321−i32−1+i32−1+i321−i321−i32−1+i32−1+i32
χ51111111111-1-11111-1-1-1-1-1-111−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i321+i321+i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+i321+i321+i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i321−i321−i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−i321−i321−i32−1+i32−1+i32
χ52111111111-1-111-1-1-1-11111-1-1−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i321+i321+i32−1−i32−1−i321+i321+i321+i321+i32−1−i32−1−i32−1−i32−1−i321+i321+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i321−i321−i32−1+i32−1+i321−i321−i321−i321−i32−1+i32−1+i32−1+i32−1+i321−i321−i32
χ53111111111-1-1-1-1111111-1-1-1-1−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−i32
χ54111111111-1-1-1-1-1-111-1-11111−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+i321+i321+i32−1−i32−1−i321+i321+i32−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−i321−i321−i32−1+i32−1+i321−i321−i32−1+i32−1+i32−1+i32−1+i32
χ5522222-2-2-2-2000000002i−2i0000−1−i3−1−i3−1−i3−1−i3−1−i31+i31+i31+i31+i3000000002ζ11−2ζ110000−1+i3−1+i3−1+i3−1+i3−1+i31−i31−i31−i31−i3000000002ζ7−2ζ70000
χ5622222-2-2-2-200000000−2i2i0000−1−i3−1−i3−1−i3−1−i3−1−i31+i31+i31+i31+i300000000−2ζ112ζ110000−1+i3−1+i3−1+i3−1+i3−1+i31−i31−i31−i31−i300000000−2ζ72ζ70000
χ57222-2-22-2-22002i−2i0000000000−1−i3−1−i3−1−i31+i31+i3−1−i31+i31+i3−1−i3002ζ11−2ζ110000000000−1+i3−1+i3−1+i31−i31−i3−1+i31−i31−i3−1+i3002ζ7−2ζ70000000000
χ58222-2-22-2-2200−2i2i0000000000−1−i3−1−i3−1−i31+i31+i3−1−i31+i31+i3−1−i300−2ζ112ζ110000000000−1+i3−1+i3−1+i31−i31−i3−1+i31−i31−i3−1+i300−2ζ72ζ70000000000
χ59222-2-2-222-200000000002i−2i00−1−i3−1−i3−1−i31+i31+i31+i3−1−i3−1−i31+i300000000002ζ11−2ζ1100−1+i3−1+i3−1+i31−i31−i31−i3−1+i3−1+i31−i300000000002ζ7−2ζ700
χ60222-2-2-222-20000000000−2i2i00−1−i3−1−i3−1−i31+i31+i31+i3−1−i3−1−i31+i30000000000−2ζ112ζ1100−1+i3−1+i3−1+i31−i31−i31−i3−1+i3−1+i31−i30000000000−2ζ72ζ700
χ6122-22-222-2-200002i−2i00000000−1−i3−1−i31+i3−1−i31+i3−1−i3−1−i31+i31+i300002ζ11−2ζ1100000000−1+i3−1+i31−i3−1+i31−i3−1+i3−1+i31−i31−i300002ζ7−2ζ700000000
χ6222-22-222-2-20000−2i2i00000000−1−i3−1−i31+i3−1−i31+i3−1−i3−1−i31+i31+i30000−2ζ112ζ1100000000−1+i3−1+i31−i3−1+i31−i3−1+i3−1+i31−i31−i30000−2ζ72ζ700000000
χ6322-22-2-2-2220000002-2000000−1−i3−1−i31+i3−1−i31+i31+i31+i3−1−i3−1−i3000000−1−i31+i3000000−1+i3−1+i31−i3−1+i31−i31−i31−i3−1+i3−1+i3000000−1+i31−i3000000
χ6422-22-2-2-222000000-22000000−1−i3−1−i31+i3−1−i31+i31+i31+i3−1−i3−1−i30000001+i3−1−i3000000−1+i3−1+i31−i3−1+i31−i31−i31−i3−1+i3−1+i30000001−i3−1+i3000000
χ6522-2-222-22-20000000000002i−2i−1−i3−1−i31+i31+i3−1−i3−1−i31+i3−1−i31+i30000000000002ζ11−2ζ11−1+i3−1+i31−i31−i3−1+i3−1+i31−i3−1+i31−i30000000000002ζ7−2ζ7
χ6622-2-222-22-2000000000000−2i2i−1−i3−1−i31+i31+i3−1−i3−1−i31+i3−1−i31+i3000000000000−2ζ112ζ11−1+i3−1+i31−i31−i3−1+i3−1+i31−i3−1+i31−i3000000000000−2ζ72ζ7
χ6722-2-22-22-222-2000000000000−1−i3−1−i31+i31+i3−1−i31+i3−1−i31+i3−1−i3−1−i31+i3000000000000−1+i3−1+i31−i31−i3−1+i31−i3−1+i31−i3−1+i3−1+i31−i3000000000000
χ6822-2-22-22-22-22000000000000−1−i3−1−i31+i31+i3−1−i31+i3−1−i31+i3−1−i31+i3−1−i3000000000000−1+i3−1+i31−i31−i3−1+i31−i3−1+i31−i3−1+i31−i3−1+i3000000000000
χ698-8000000000000000000000−4−4i34+4i3000000000000000000000−4+4i34−4i3000000000000000000000

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