Finite Group Databasebeta

← Group #13166159

Character table — Group #13166159

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78
size11222224444444444668888888888121212121212121212121616161616161616161616161818242436363636363648484848484848484848484872727272108
order1233466333666121212122433336666121224666612121212336612121212121212128861224661212666666121212121212242424248
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111-111111-1-11111111111111-1-111-11-1-111111111-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111-111-1-111111111111111111-1-1111-111-1-1-1-1-1-1-1-1111111-1-1-1-1-1
χ411111111111111111111111111111-1-11-1-111-1-111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111
χ511111111−1−i32−1+i321−1−i32−1+i32111111−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i321111111111−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1−i32−1+i32−1+i321111111111−1−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+i321
χ611111111−1−i32−1+i321−1−i32−1+i32111111−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i321-111111-1-11−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32-1-111-11-1-111−1−i32−1+i32−1−i32−1−i32−1+i32−1+i321+i321−i321+i321+i321−i321−i321+i321+i321−i321−i32-1
χ711111111−1−i32−1+i321−1−i32−1+i32111111−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32-111-1-111111−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32-1-1111-111-1-11+i321−i321+i321+i321−i321−i32−1−i32−1+i32−1−i32−1−i32−1+i32−1+i321+i321+i321−i321−i32-1
χ811111111−1−i32−1+i321−1−i32−1+i32111111−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32-1-11-1-111-1-11−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1−i32−1+i32−1+i321111-1-1-1-1-1-11+i321−i321+i321+i321−i321−i321+i321−i321+i321+i321−i321−i32−1−i32−1−i32−1+i32−1+i321
χ911111111−1+i32−1−i321−1+i32−1−i32111111−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i321111111111−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1+i32−1−i32−1−i321111111111−1+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−i321
χ1011111111−1+i32−1−i321−1+i32−1−i32111111−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i321-111111-1-11−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32-1-111-11-1-111−1+i32−1−i32−1+i32−1+i32−1−i32−1−i321−i321+i321−i321−i321+i321+i321−i321−i321+i321+i32-1
χ1111111111−1+i32−1−i321−1+i32−1−i32111111−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32-111-1-111111−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32-1-1111-111-1-11−i321+i321−i321−i321+i321+i32−1+i32−1−i32−1+i32−1+i32−1−i32−1−i321−i321−i321+i321+i32-1
χ1211111111−1+i32−1−i321−1+i32−1−i32111111−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32-1-11-1-111-1-11−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1+i32−1−i32−1−i321111-1-1-1-1-1-11−i321+i321−i321−i321+i321+i321−i321+i321−i321−i321+i321+i32−1+i32−1+i32−1−i32−1−i321
χ132222-222222222-2-2-2-2-2222222222-2-200-200-220022222-2-2-2-2-2-2-2-200-2200000000000000000000000
χ142222-2222−1−i3−1+i32−1−i3−1+i3-2-2-2-2-22−1−i3−1+i3−1−i3−1+i3−1−i3−1+i3−1−i3−1+i31+i31−i300-200-22002−1−i3−1+i3−1−i3−1+i31+i31−i31+i31−i31+i31+i31−i31−i300-2200000000000000000000000
χ152222-2222−1+i3−1−i32−1+i3−1−i3-2-2-2-2-22−1+i3−1−i3−1+i3−1−i3−1+i3−1−i3−1+i3−1−i31−i31+i300-200-22002−1+i3−1−i3−1+i3−1−i31−i31+i31−i31+i31−i31−i31+i31+i300-2200000000000000000000000
χ16222-12-12-122-122-12-1-122-1-12222-1-12202200-1-1-1-12-1-1-1-122-1-1-1-1-1-100-1-120-1-10000000022-1-1-1-100000
χ17222-12-12-122-122-12-1-122-1-12222-1-1220-2200-1-1112-1-1-1-122-1-1-1-1-1-100-1-1-201100000000-2-2111100000
χ18222-12-12-1−1−i3−1+i3-1−1−i3−1+i3-12-1-1221+i321−i32−1−i3−1+i3−1−i3−1+i31+i321−i32−1−i3−1+i302200-1-1-1-121+i321−i321+i321−i32−1−i3−1+i31+i321−i321+i321+i321−i321−i3200-1-120-1-100000000−1−i3−1+i31+i321+i321−i321−i3200000
χ19222-12-12-1−1−i3−1+i3-1−1−i3−1+i3-12-1-1221+i321−i32−1−i3−1+i3−1−i3−1+i31+i321−i32−1−i3−1+i30-2200-1-11121+i321−i321+i321−i32−1−i3−1+i31+i321−i321+i321+i321−i321−i3200-1-1-2011000000001+i31−i3−1−i32−1−i32−1+i32−1+i3200000
χ20222-12-12-1−1+i3−1−i3-1−1+i3−1−i3-12-1-1221−i321+i32−1+i3−1−i3−1+i3−1−i31−i321+i32−1+i3−1−i302200-1-1-1-121−i321+i321−i321+i32−1+i3−1−i31−i321+i321−i321−i321+i321+i3200-1-120-1-100000000−1+i3−1−i31−i321−i321+i321+i3200000
χ21222-12-12-1−1+i3−1−i3-1−1+i3−1−i3-12-1-1221−i321+i32−1+i3−1−i3−1+i3−1−i31−i321+i32−1+i3−1−i30-2200-1-11121−i321+i321−i321+i32−1+i3−1−i31−i321+i321−i321−i321+i321+i3200-1-1-2011000000001−i31+i3−1+i32−1+i32−1−i32−1−i3200000
χ22222-1-2-12-122-1221-211-22-1-12222-1-1-2-200-2001-1−i3i32-1-1-1-1-2-2111111001-100−i3i30000000000−i3i3−i3i300000
χ23222-1-2-12-122-1221-211-22-1-12222-1-1-2-200-2001-1i3−i32-1-1-1-1-2-2111111001-100i3−i30000000000i3−i3i3−i300000
χ24222-1-2-12-1−1−i3−1+i3-1−1−i3−1+i31-211-221+i321−i32−1−i3−1+i3−1−i3−1+i31+i321−i321+i31−i300-2001-1−i3i321+i321−i321+i321−i321+i31−i3−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32001-100−i3i30000000000−3+i323−i323+i32−3−i3200000
χ25222-1-2-12-1−1−i3−1+i3-1−1−i3−1+i31-211-221+i321−i32−1−i3−1+i3−1−i3−1+i31+i321−i321+i31−i300-2001-1i3−i321+i321−i321+i321−i321+i31−i3−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32001-100i3−i300000000003−i32−3+i32−3−i323+i3200000
χ26222-1-2-12-1−1+i3−1−i3-1−1+i3−1−i31-211-221−i321+i32−1+i3−1−i3−1+i3−1−i31−i321+i321−i31+i300-2001-1−i3i321−i321+i321−i321+i321−i31+i3−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32001-100−i3i300000000003+i32−3−i32−3+i323−i3200000
χ27222-1-2-12-1−1+i3−1−i3-1−1+i3−1−i31-211-221−i321+i32−1+i3−1−i3−1+i3−1−i31−i321+i321−i31+i300-2001-1i3−i321−i321+i321−i321+i321−i31+i3−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32001-100i3−i30000000000−3−i323+i323−i32−3+i3200000
χ2822-1222-1-122-1222-1-1-12222-1-1-1-1222220-1-1-12200-1-1-1-1-1-1-122-1-1-1-100-1-10200-1-122-1-1-1-100000000000
χ2922-1222-1-122-1222-1-1-12222-1-1-1-12222-20-1112200-1-1-1-1-1-1-122-1-1-1-100-1-10-20011-2-2111100000000000
χ3022-1222-1-1−1−i3−1+i3-1−1−i3−1+i32-1-1-122−1−i3−1+i31+i321−i321+i321−i32−1−i3−1+i3−1−i3−1+i320-1-1-12200-11+i321−i321+i321−i321+i321−i32−1−i3−1+i31+i321+i321−i321−i3200-1-10200-1-1−1−i3−1+i31+i321+i321−i321−i3200000000000
χ3122-1222-1-1−1−i3−1+i3-1−1−i3−1+i32-1-1-122−1−i3−1+i31+i321−i321+i321−i32−1−i3−1+i3−1−i3−1+i3-20-1112200-11+i321−i321+i321−i321+i321−i32−1−i3−1+i31+i321+i321−i321−i3200-1-10-200111+i31−i3−1−i32−1−i32−1+i32−1+i3200000000000
χ3222-1222-1-1−1+i3−1−i3-1−1+i3−1−i32-1-1-122−1+i3−1−i31−i321+i321−i321+i32−1+i3−1−i3−1+i3−1−i320-1-1-12200-11−i321+i321−i321+i321−i321+i32−1+i3−1−i31−i321−i321+i321+i3200-1-10200-1-1−1+i3−1−i31−i321−i321+i321+i3200000000000
χ3322-1222-1-1−1+i3−1−i3-1−1+i3−1−i32-1-1-122−1+i3−1−i31−i321+i321−i321+i32−1+i3−1−i3−1+i3−1−i3-20-1112200-11−i321+i321−i321+i321−i321+i32−1+i3−1−i31−i321−i321+i321+i3200-1-10-200111−i31+i3−1+i32−1+i32−1−i32−1−i3200000000000
χ3422-12-22-1-122-122-2111-2222-1-1-1-122-2-2001−i3i3-2200-1-1-1-1-111-2-21111001-10000−i3i300−i3i3−i3i300000000000
χ3522-12-22-1-122-122-2111-2222-1-1-1-122-2-2001i3−i3-2200-1-1-1-1-111-2-21111001-10000i3−i300i3−i3i3−i300000000000
χ3622-12-22-1-1−1−i3−1+i3-1−1−i3−1+i3-2111-22−1−i3−1+i31+i321−i321+i321−i32−1−i3−1+i31+i31−i3001−i3i3-2200-11+i321−i321+i321−i32−1−i32−1+i321+i31−i3−1−i32−1−i32−1+i32−1+i32001-10000−i3i300−3+i323−i323+i32−3−i3200000000000
χ3722-12-22-1-1−1−i3−1+i3-1−1−i3−1+i3-2111-22−1−i3−1+i31+i321−i321+i321−i32−1−i3−1+i31+i31−i3001i3−i3-2200-11+i321−i321+i321−i32−1−i32−1+i321+i31−i3−1−i32−1−i32−1+i32−1+i32001-10000i3−i3003−i32−3+i32−3−i323+i3200000000000
χ3822-12-22-1-1−1+i3−1−i3-1−1+i3−1−i3-2111-22−1+i3−1−i31−i321+i321−i321+i32−1+i3−1−i31−i31+i3001−i3i3-2200-11−i321+i321−i321+i32−1+i32−1−i321−i31+i3−1+i32−1+i32−1−i32−1−i32001-10000−i3i3003+i32−3−i32−3+i323−i3200000000000
χ3922-12-22-1-1−1+i3−1−i3-1−1+i3−1−i3-2111-22−1+i3−1−i31−i321+i321−i321+i32−1+i3−1−i31−i31+i3001i3−i3-2200-11−i321+i321−i321+i32−1+i32−1−i321−i31+i3−1+i32−1+i32−1−i32−1−i32001-10000i3−i300−3−i323+i323−i32−3+i3200000000000
χ4033333333003003333-1-1000000000033-133-1-133-100000000000033-1-1-1-1-1-1-1-10000000000000000-1
χ4133333333003003333-1-100000000003-3-133-1-1-3-3-1000000000000-3-3-1-11-111-1-100000000000000001
χ4233333333003003333-1-10000000000-33-1-3-3-1-133-1000000000000-3-3-1-1-11-1-11100000000000000001
χ4333333333003003333-1-10000000000-3-3-1-3-3-1-1-3-3-100000000000033-1-11111110000000000000000-1
χ4444-2-24-2-2144144-2-21144-2-2-2-2-2-2-2-24400-200-2-200-21111-2-2-2-21111001100000000000000000000000
χ4544-2-24-2-21−2−2i3−2+2i31−2−2i3−2+2i3-2-211441+i31−i31+i31−i31+i31−i31+i31−i3−2−2i3−2+2i300-200-2-200-2−1−i32−1+i32−1−i32−1+i321+i31−i31+i31−i3−1−i32−1−i32−1+i32−1+i32001100000000000000000000000
χ4644-2-24-2-21−2+2i3−2−2i31−2+2i3−2−2i3-2-211441−i31+i31−i31+i31−i31+i31−i31+i3−2+2i3−2−2i300-200-2-200-2−1+i32−1−i32−1+i32−1−i321−i31+i31−i31+i3−1+i32−1+i32−1−i32−1−i32001100000000000000000000000
χ4744-2-2-4-2-214414422-1-1-44-2-2-2-2-2-2-2-2-4-4002002-200-211112222-1-1-1-100-1100000000000000000000000
χ4844-2-2-4-2-21−2−2i3−2+2i31−2−2i3−2+2i322-1-1-441+i31−i31+i31−i31+i31−i31+i31−i32+2i32−2i3002002-200-2−1−i32−1+i32−1−i32−1+i32−1−i3−1+i3−1−i3−1+i31+i321+i321−i321−i3200-1100000000000000000000000
χ4944-2-2-4-2-21−2+2i3−2−2i31−2+2i3−2−2i322-1-1-441−i31+i31−i31+i31−i31+i31−i31+i32−2i32+2i3002002-200-2−1+i32−1−i32−1+i32−1−i32−1+i3−1−i3−1+i3−1−i31−i321−i321+i321+i3200-1100000000000000000000000
χ504-4440-4-44-2-2-422000000-2-2-2-22222000000000000-2-22200000000−2i22i200000000000000000000−i2i2−i2i20
χ514-4440-4-44-2-2-422000000-2-2-2-22222000000000000-2-222000000002i2−2i200000000000000000000i2−i2i2−i20
χ524-4440-4-441+i31−i3-4−1−i3−1+i30000001+i31−i31+i31−i3−1−i3−1+i3−1−i3−1+i30000000000001+i31−i3−1−i3−1+i300000000−2i22i200000000000000000000ζ7+ζ13−ζ7−ζ13ζ5+ζ23−ζ5−ζ230
χ534-4440-4-441+i31−i3-4−1−i3−1+i30000001+i31−i31+i31−i3−1−i3−1+i3−1−i3−1+i30000000000001+i31−i3−1−i3−1+i3000000002i2−2i200000000000000000000−ζ7−ζ13ζ7+ζ13−ζ5−ζ23ζ5+ζ230
χ544-4440-4-441−i31+i3-4−1+i3−1−i30000001−i31+i31−i31+i3−1+i3−1−i3−1+i3−1−i30000000000001−i31+i3−1+i3−1−i300000000−2i22i200000000000000000000ζ5+ζ23−ζ5−ζ23ζ7+ζ13−ζ7−ζ130
χ554-4440-4-441−i31+i3-4−1+i3−1−i30000001−i31+i31−i31+i3−1+i3−1−i3−1+i3−1−i30000000000001−i31+i3−1+i3−1−i3000000002i2−2i200000000000000000000−ζ5−ζ23ζ5+ζ23−ζ7−ζ13ζ7+ζ130
χ566666-666600600-6-6-6-62-20000000000002002-200-2000000000000002-200000000000000000000000
χ57666-36-36-300-300-36-3-3-2-2000000000006-20011-3-3-20000000000000011-20110000000000000000000
χ58666-36-36-300-300-36-3-3-2-200000000000-6-2001133-2000000000000001120-1-10000000000000000000
χ59666-3-6-36-300-3003-6332-2000000000000200-11−3i33i3-200000000000000-1100i3−i30000000000000000000
χ60666-3-6-36-300-3003-6332-2000000000000200-113i3−3i3-200000000000000-1100−i3i30000000000000000000
χ6166-3666-3-300-3006-3-3-3-2-20000000000601-3-3-2-200100000000000000110-2001100000000000000000
χ6266-3666-3-300-3006-3-3-3-2-20000000000-60133-2-200100000000000000110200-1-100000000000000000
χ6366-36-66-3-300-300-63332-2000000000000-1−3i33i32-200100000000000000-110000i3−i300000000000000000
χ6466-36-66-3-300-300-63332-2000000000000-13i3−3i32-200100000000000000-110000−i3i300000000000000000
χ658-88-404-8-4-4-444400000022-4-444-2-200000000000022-2-200000000000000000000000000000000000
χ668-88-404-8-42+2i32−2i34−2−2i3−2+2i3000000−1−i3−1+i32+2i32−2i3−2−2i3−2+2i31+i31−i3000000000000−1−i3−1+i31+i31−i300000000000000000000000000000000000
χ678-88-404-8-42−2i32+2i34−2+2i3−2−2i3000000−1+i3−1−i32−2i32+2i3−2+2i3−2−2i31−i31+i3000000000000−1+i3−1−i31−i31+i300000000000000000000000000000000000
χ688-8-480-84-4-4-4444000000-4-422-2-24400000000000022-2-200000000000000000000000000000000000
χ698-8-480-84-42+2i32−2i34−2−2i3−2+2i30000002+2i32−2i3−1−i3−1+i31+i31−i3−2−2i3−2+2i3000000000000−1−i3−1+i31+i31−i300000000000000000000000000000000000
χ708-8-480-84-42−2i32+2i34−2+2i3−2−2i30000002−2i32+2i3−1+i3−1−i31−i31+i3−2+2i3−2−2i3000000000000−1+i3−1−i31−i31+i300000000000000000000000000000000000
χ718-8-4-40442-4-4-244006i−6i002222-2-2-2-2000000000000-1-11100003i−3i3i−3i000000000000000000000000000
χ728-8-4-40442-4-4-24400−6i6i002222-2-2-2-2000000000000-1-1110000−3i3i−3i3i000000000000000000000000000
χ738-8-4-404422+2i32−2i3-2−2−2i3−2+2i3006i−6i00−1−i3−1+i3−1−i3−1+i31+i31−i31+i31−i30000000000001+i321−i32−1−i32−1+i3200003ζ22−3ζ223ζ14−3ζ14000000000000000000000000000
χ748-8-4-404422+2i32−2i3-2−2−2i3−2+2i300−6i6i00−1−i3−1+i3−1−i3−1+i31+i31−i31+i31−i30000000000001+i321−i32−1−i32−1+i320000−3ζ223ζ22−3ζ143ζ14000000000000000000000000000
χ758-8-4-404422−2i32+2i3-2−2+2i3−2−2i3006i−6i00−1+i3−1−i3−1+i3−1−i31−i31+i31−i31+i30000000000001−i321+i32−1+i32−1−i3200003ζ14−3ζ143ζ22−3ζ22000000000000000000000000000
χ768-8-4-404422−2i32+2i3-2−2+2i3−2−2i300−6i6i00−1+i3−1−i3−1+i3−1−i31−i31+i31−i31+i30000000000001−i321+i32−1+i32−1−i320000−3ζ143ζ14−3ζ223ζ22000000000000000000000000000
χ771212-6-612-6-6300300-6-633-4-40000000000002002200200000000000000-1-100000000000000000000000
χ781212-6-6-12-6-630030066-3-34-4000000000000-200-22002000000000000001-100000000000000000000000

Here ζ is a primitive root of unity of order 24 (ζ24 = 1); i = ζ6.