Finite Group Databasebeta

← Group #10596625

Character table — Group #10596625

Order 576.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57
size112222233444444466666668888888888121212121212121216161616161618181818242424242424
order1222346443366661222444443366666612126121212121212126666121222246612121212
χ1111111111111111111111111111111111111111111111111111111111
χ2111111111−1−i32−1+i3211−1−i32−1+i3211111111−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1+i32−1−i32−1+i321111−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1+i321111−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32
χ3111111111−1+i32−1−i3211−1+i32−1−i3211111111−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1−i32−1+i32−1−i321111−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1−i321111−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32
χ41111111-1-111111111-1111-1-111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1
χ51111111-1-1−1−i32−1+i3211−1−i32−1+i3211-1111-1-1−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1+i32−1−i32−1+i3211111+i321+i321−i321−i32−1−i32−1−i32−1+i32−1+i32−1−i32−1+i32-1-1-1-11+i321−i321+i321+i321−i321−i32
χ61111111-1-1−1+i32−1−i3211−1+i32−1−i3211-1111-1-1−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1−i32−1+i32−1−i3211111−i321−i321+i321+i32−1+i32−1+i32−1−i32−1−i32−1+i32−1−i32-1-1-1-11−i321+i321−i321−i321+i321+i32
χ7111-11-1111111-111-1-1-111-11-1111-11-111-1-1-111-111111-11-1-1-111-1-1-1-11-11-1
χ8111-11-1111−1−i32−1+i321-1−1−i32−1+i32-1-1-111-11-1−1−i32−1+i32−1−i321+i32−1+i321−i32−1−i32−1+i321+i321−i32-111-1−1−i32−1−i32−1+i32−1+i32−1−i321+i32−1+i321−i321+i321−i3211-1-11+i321−i32−1−i321+i32−1+i321−i32
χ9111-11-1111−1+i32−1−i321-1−1+i32−1−i32-1-1-111-11-1−1+i32−1−i32−1+i321−i32−1−i321+i32−1+i32−1−i321−i321+i32-111-1−1+i32−1+i32−1−i32−1−i32−1+i321−i32−1−i321+i321−i321+i3211-1-11−i321+i32−1+i321−i32−1−i321+i32
χ10111-11-11-1-1111-111-1-1111-1-11111-11-111-1-1-111-1-1-1-1-11-11-1-1-1-1-11111-11-11
χ11111-11-11-1-1−1−i32−1+i321-1−1−i32−1+i32-1-1111-1-11−1−i32−1+i32−1−i321+i32−1+i321−i32−1−i32−1+i321+i321−i32-111-11+i321+i321−i321−i32−1−i321+i32−1+i321−i321+i321−i32-1-111−1−i32−1+i321+i32−1−i321−i32−1+i32
χ12111-11-11-1-1−1+i32−1−i321-1−1+i32−1−i32-1-1111-1-11−1+i32−1−i32−1+i321−i32−1−i321+i32−1+i32−1−i321−i321+i32-111-11−i321−i321+i321+i32−1+i321−i32−1−i321+i321−i321+i32-1-111−1+i32−1−i321−i32−1+i321+i32−1−i32
χ1311-111-111111-1111-1-1-11-11-1111-11-1111-1-1-11-111111-11-11-1-11-11-1-1-1-11-11
χ1411-111-1111−1−i32−1+i32-11−1−i32−1+i32-1-1-11-11-11−1−i32−1+i321+i32−1−i321−i32−1+i32−1−i32−1+i321+i321−i32-11-11−1−i32−1−i32−1+i32−1+i321+i32−1−i321−i32−1+i321+i321−i321-11-11+i321−i321+i32−1−i321−i32−1+i32
χ1511-111-1111−1+i32−1−i32-11−1+i32−1−i32-1-1-11-11-11−1+i32−1−i321−i32−1+i321+i32−1−i32−1+i32−1−i321−i321+i32-11-11−1+i32−1+i32−1−i32−1−i321−i32−1+i321+i32−1−i321−i321+i321-11-11−i321+i321−i32−1+i321+i32−1−i32
χ1611-111-11-1-111-1111-1-111-111-111-11-1111-1-1-11-11-1-1-1-1-11-11-1-1-11-11111-11-1
χ1711-111-11-1-1−1−i32−1+i32-11−1−i32−1+i32-1-111-111-1−1−i32−1+i321+i32−1−i321−i32−1+i32−1−i32−1+i321+i321−i32-11-111+i321+i321−i321−i321+i32−1−i321−i32−1+i321+i321−i32-11-11−1−i32−1+i32−1−i321+i32−1+i321−i32
χ1811-111-11-1-1−1+i32−1−i32-11−1+i32−1−i32-1-111-111-1−1+i32−1−i321−i32−1+i321+i32−1−i32−1+i32−1−i321−i321+i32-11-111−i321−i321+i321+i321−i32−1+i321+i32−1−i321−i321+i32-11-11−1+i32−1−i32−1+i321−i32−1−i321+i32
χ1911-1-11111111-1-1111111-1-1-1-111-1-1-1-1111111-1-11111-1-1-1-1111-1-1111-1-1-1-1
χ2011-1-111111−1−i32−1+i32-1-1−1−i32−1+i321111-1-1-1-1−1−i32−1+i321+i321+i321−i321−i32−1−i32−1+i32−1−i32−1+i3211-1-1−1−i32−1−i32−1+i32−1+i321+i321+i321−i321−i32−1−i32−1+i321-1-11−1−i32−1+i321+i321+i321−i321−i32
χ2111-1-111111−1+i32−1−i32-1-1−1+i32−1−i321111-1-1-1-1−1+i32−1−i321−i321−i321+i321+i32−1+i32−1−i32−1+i32−1−i3211-1-1−1+i32−1+i32−1−i32−1−i321−i321−i321+i321+i32−1+i32−1−i321-1-11−1+i32−1−i321−i321−i321+i321+i32
χ2211-1-1111-1-111-1-11111-11-1-11111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-111-111-1-1-11111
χ2311-1-1111-1-1−1−i32−1+i32-1-1−1−i32−1+i3211-11-1-111−1−i32−1+i321+i321+i321−i321−i32−1−i32−1+i32−1−i32−1+i3211-1-11+i321+i321−i321−i321+i321+i321−i321−i32−1−i32−1+i32-111-11+i321−i32−1−i32−1−i32−1+i32−1+i32
χ2411-1-1111-1-1−1+i32−1−i32-1-1−1+i32−1−i3211-11-1-111−1+i32−1−i321−i321−i321+i321+i32−1+i32−1−i32−1+i32−1−i3211-1-11−i321−i321+i321+i321−i321−i321+i321+i32−1+i32−1−i32-111-11−i321+i32−1+i32−1+i32−1−i32−1−i32
χ252222-12-10022-1-122-12022200-1-12222-1-122-1-1-1-10000-1-1-1-1-1-10000000000
χ262222-12-100−1−i3−1+i3-1-1−1−i3−1+i3-120222001+i321−i32−1−i3−1−i3−1+i3−1+i31+i321−i32−1−i3−1+i3-1-1-1-100001+i321+i321−i321−i321+i321−i320000000000
χ272222-12-100−1+i3−1−i3-1-1−1+i3−1−i3-120222001−i321+i32−1+i3−1+i3−1−i3−1−i31−i321+i32−1+i3−1−i3-1-1-1-100001−i321−i321+i321+i321−i321+i320000000000
χ28222-2-1-2-10022-11221-2022-200-1-12-22-2-1-1-2-21-1-110000-11-11110000000000
χ29222-2-1-2-100−1−i3−1+i3-11−1−i3−1+i31-2022-2001+i321−i32−1−i31+i3−1+i31−i31+i321−i321+i31−i31-1-1100001+i32−1−i321−i32−1+i32−1−i32−1+i320000000000
χ30222-2-1-2-100−1+i3−1−i3-11−1+i3−1−i31-2022-2001−i321+i32−1+i31−i3−1−i31+i31−i321+i321−i31+i31-1-1100001−i32−1+i321+i32−1−i32−1+i32−1−i320000000000
χ3122-22-1-2-100221-1221-202-2200-1-1-22-22-1-1-2-21-11-100001-11-1110000000000
χ3222-22-1-2-100−1−i3−1+i31-1−1−i3−1+i31-202-22001+i321−i321+i3−1−i31−i3−1+i31+i321−i321+i31−i31-11-10000−1−i321+i32−1+i321−i32−1−i32−1+i320000000000
χ3322-22-1-2-100−1+i3−1−i31-1−1+i3−1−i31-202-22001−i321+i321−i3−1+i31+i3−1−i31−i321+i321−i31+i31-11-10000−1+i321−i32−1−i321+i32−1+i32−1−i320000000000
χ3422-2-2-12-100221122-1202-2-200-1-1-2-2-2-2-1-122-1-11100001111-1-10000000000
χ3522-2-2-12-100−1−i3−1+i311−1−i3−1+i3-1202-2-2001+i321−i321+i31+i31−i31−i31+i321−i32−1−i3−1+i3-1-1110000−1−i32−1−i32−1+i32−1+i321+i321−i320000000000
χ3622-2-2-12-100−1+i3−1−i311−1+i3−1−i3-1202-2-2001−i321+i321−i31−i31+i31+i31−i321+i32−1+i3−1−i3-1-1110000−1+i32−1+i32−1−i32−1−i321−i321+i320000000000
χ373333333330033003-13-1-1-1330000000000-1-1-1-10000000000-1-1-1-1000000
χ383333333-3-30033003-1-3-1-1-1-3-30000000000-1-1-1-100000000001111000000
χ39333-33-3333003-300-31-3-1-113-300000000001-1-110000000000-1-111000000
χ40333-33-33-3-3003-300-313-1-11-3300000000001-1-11000000000011-1-1000000
χ4133-333-333300-3300-31-3-11-1-3300000000001-11-10000000000-11-11000000
χ4233-333-33-3-300-3300-313-11-13-300000000001-11-100000000001-11-1000000
χ4333-3-33333300-3-3003-13-111-3-30000000000-1-1110000000000-111-1000000
χ4433-3-3333-3-300-3-3003-1-3-111330000000000-1-11100000000001-1-11000000
χ454-40040-44i−4i-2-2002200000000-2-20000220000002i−2i2i−2i0000000000000000
χ464-40040-44i−4i1+i31−i300−1−i3−1+i3000000001+i31−i30000−1−i3−1+i30000002ζ11−2ζ112ζ7−2ζ70000000000000000
χ474-40040-44i−4i1−i31+i300−1+i3−1−i3000000001−i31+i30000−1+i3−1−i30000002ζ7−2ζ72ζ11−2ζ110000000000000000
χ484-40040-4−4i4i-2-2002200000000-2-2000022000000−2i2i−2i2i0000000000000000
χ494-40040-4−4i4i1+i31−i300−1−i3−1+i3000000001+i31−i30000−1−i3−1+i3000000−2ζ112ζ11−2ζ72ζ70000000000000000
χ504-40040-4−4i4i1−i31+i300−1+i3−1−i3000000001−i31+i30000−1+i3−1−i3000000−2ζ72ζ7−2ζ112ζ110000000000000000
χ516666-36-30000-3-300-3-20-2-2-2000000000000111100000000000000000000
χ52666-6-3-6-30000-3300320-2-22000000000000-111-100000000000000000000
χ5366-66-3-6-300003-300320-22-2000000000000-11-1100000000000000000000
χ5466-6-6-36-300003300-3-20-22200000000000011-1-100000000000000000000
χ558-800-40400-4-4004400000000220000-2-200000000000000000000000000
χ568-800-404002+2i32−2i300−2−2i3−2+2i300000000−1−i3−1+i300001+i31−i300000000000000000000000000
χ578-800-404002−2i32+2i300−2+2i3−2−2i300000000−1+i3−1−i300001−i31+i300000000000000000000000000

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