Finite Group Databasebeta

← Group #13146606

Character table — Group #13146606

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74
size11112222222222121212121212121218181818181818181818181818181818181818181818181818181818181818181818181824242424727272727272727272727272
order12223446661212121233666666224466668888888812121212242424242424242424242424242424241212121244441212121212121212
χ111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111-11-111-1-111-1-1
χ4111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-11-11-1-111-1-111
χ511111-1-1111-1-1-1-111111111-1-111-1-1-1-11111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-1
χ611111-1-1111-1-1-1-111111111-1-111-1-1-1-11111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111
χ711111-1-1111-1-1-1-111111111-1-111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-11-1-1111-1-1-1-111
χ811111-1-1111-1-1-1-111111111-1-111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-111-1-1-11111-1-1
χ92222222222222222222222-2-2-2-2-2-2-2-200000000-2-2-2-200000000000000002222000000000000
χ1022222-2-2222-2-2-2-22222222222-2-2222200000000-2-2-2-20000000000000000-2-2-2-2000000000000
χ1122-2-22002-2-200002222-2-2-2-22-20022-2-222−2−222−2−200002222−2−2−2−22222−2−2−2−20000000000000000
χ1222-2-22002-2-200002222-2-2-2-22-20022-2-2−2−222−2−2220000−2−2−2−22222−2−2−2−222220000000000000000
χ1322-2-22002-2-200002222-2-2-2-2-2200-2-22222−2−2−2−22200002222−2−2−2−2−2−2−2−222220000000000000000
χ1422-2-22002-2-200002222-2-2-2-2-2200-2-222−2−22222−2−20000−2−2−2−222222222−2−2−2−20000000000000000
χ152-22-222i−2i-22-22i2i−2i−2i22-2-222-2-2000000002−22−2−i2i2−i2i2000022−2−222−2−2−i2−i2i2i2−i2−i2i2i22i2i−2i−2i000000000000
χ162-22-222i−2i-22-22i2i−2i−2i22-2-222-2-200000000−22−22i2−i2i2−i20000−2−222−2−222i2i2−i2−i2i2i2−i2−i22i2i−2i−2i000000000000
χ172-22-22−2i2i-22-2−2i−2i2i2i22-2-222-2-2000000002−22−2i2−i2i2−i2000022−2−222−2−2i2i2−i2−i2i2i2−i2−i2−2i−2i2i2i000000000000
χ182-22-22−2i2i-22-2−2i−2i2i2i22-2-222-2-200000000−22−22−i2i2−i2i20000−2−222−2−222−i2−i2i2i2−i2−i2i2i2−2i−2i2i2i000000000000
χ192-2-22200-2-22000022-2-2-2-222002-2000000002i−2i−2i2i22-2-2000000002i2i−2i−2i−2i−2i2i2i0000000000000000
χ202-2-22200-2-22000022-2-2-2-222002-200000000−2i2i2i−2i22-2-200000000−2i−2i2i2i2i2i−2i−2i0000000000000000
χ212-2-22200-2-22000022-2-2-2-22200-2200002-2-220000-2-22222-2-2-2-222000000000000000000000000
χ222-2-22200-2-22000022-2-2-2-22200-220000-222-20000-2-222-2-22222-2-2000000000000000000000000
χ23444444444444441-21-21-21-20000000000000000000000000000000000001-21-2020200-1-100-1-1
χ24444444444444441-21-21-21-20000000000000000000000000000000000001-21-20-20-200110011
χ2544444444444444-21-21-21-21000000000000000000000000000000000000-21-212020-1-100-1-100
χ2644444444444444-21-21-21-21000000000000000000000000000000000000-21-21-20-2011001100
χ2744444-4-4444-4-4-4-41-21-21-21-2000000000000000000000000000000000000-12-12020-200-1-10011
χ2844444-4-4444-4-4-4-41-21-21-21-2000000000000000000000000000000000000-12-120-202001100-1-1
χ2944444-4-4444-4-4-4-4-21-21-21-210000000000000000000000000000000000002-12-120-20-1-1001100
χ3044444-4-4444-4-4-4-4-21-21-21-210000000000000000000000000000000000002-12-1-20201100-1-100
χ314-44-444i−4i-44-44i4i−4i−4i1-2-121-2-12000000000000000000000000000000000000i−2i−i2i000000−i3i3003−3
χ324-44-444i−4i-44-44i4i−4i−4i1-2-121-2-12000000000000000000000000000000000000i−2i−i2i000000i3−i300−33
χ334-44-444i−4i-44-44i4i−4i−4i-212-1-212-1000000000000000000000000000000000000−2ii2i−i0000−i3i3003−300
χ344-44-444i−4i-44-44i4i−4i−4i-212-1-212-1000000000000000000000000000000000000−2ii2i−i0000i3−i300−3300
χ354-44-44−4i4i-44-4−4i−4i4i4i1-2-121-2-12000000000000000000000000000000000000−i2ii−2i000000−i3i300−33
χ364-44-44−4i4i-44-4−4i−4i4i4i1-2-121-2-12000000000000000000000000000000000000−i2ii−2i000000i3−i3003−3
χ374-44-44−4i4i-44-4−4i−4i4i4i-212-1-212-10000000000000000000000000000000000002i−i−2ii0000−i3i300−3300
χ384-44-44−4i4i-44-4−4i−4i4i4i-212-1-212-10000000000000000000000000000000000002i−i−2ii0000i3−i3003−300
χ396666-366-3-3-3-3-3-3-3000000002222-1-1-1-100000000-1-1-1-13−33−33−33−33−33−33−33−30000000000000000
χ406666-366-3-3-3-3-3-3-3000000002222-1-1-1-100000000-1-1-1-1−33−33−33−33−33−33−33−330000000000000000
χ416666-366-3-3-3-3-3-3-300000000-2-2-2-21111222222221111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000000000000000
χ426666-366-3-3-3-3-3-3-300000000-2-2-2-21111-2-2-2-2-2-2-2-2111111111111111111110000000000000000
χ436666-3-6-6-3-3-333330000000022-2-2-1-1-1-12222-2-2-2-21111-1-1-1-1-1-1-1-1111111110000000000000000
χ446666-3-6-6-3-3-333330000000022-2-2-1-1-1-1-2-2-2-22222111111111111-1-1-1-1-1-1-1-10000000000000000
χ456666-3-6-6-3-3-3333300000000-2-222111100000000-1-1-1-13−33−33−33−3−33−33−33−330000000000000000
χ466666-3-6-6-3-3-3333300000000-2-222111100000000-1-1-1-1−33−33−33−333−33−33−33−30000000000000000
χ4766-6-6-300-33333−3333−33000000002-200-1-11122−2−2−2−2223−33−3ζ5−ζ7ζ13−ζ23ζ5−ζ7ζ13−ζ23−ζ5+ζ7−ζ13+ζ23−ζ5+ζ7−ζ13+ζ23−ζ13+ζ23−ζ5+ζ7−ζ13+ζ23−ζ5+ζ7ζ13−ζ23ζ5−ζ7ζ13−ζ23ζ5−ζ70000000000000000
χ4866-6-6-300-33333−3333−33000000002-200-1-111−2−22222−2−23−33−3−ζ5+ζ7−ζ13+ζ23−ζ5+ζ7−ζ13+ζ23ζ5−ζ7ζ13−ζ23ζ5−ζ7ζ13−ζ23ζ13−ζ23ζ5−ζ7ζ13−ζ23ζ5−ζ7−ζ13+ζ23−ζ5+ζ7−ζ13+ζ23−ζ5+ζ70000000000000000
χ4966-6-6-300-33333−3333−3300000000-220011-1-122−2−222−2−2−33−33ζ13−ζ23ζ5−ζ7ζ13−ζ23ζ5−ζ7−ζ13+ζ23−ζ5+ζ7−ζ13+ζ23−ζ5+ζ7ζ5−ζ7ζ13−ζ23ζ5−ζ7ζ13−ζ23−ζ5+ζ7−ζ13+ζ23−ζ5+ζ7−ζ13+ζ230000000000000000
χ5066-6-6-300-33333−3333−3300000000-220011-1-1−2−222−2−222−33−33−ζ13+ζ23−ζ5+ζ7−ζ13+ζ23−ζ5+ζ7ζ13−ζ23ζ5−ζ7ζ13−ζ23ζ5−ζ7−ζ5+ζ7−ζ13+ζ23−ζ5+ζ7−ζ13+ζ23ζ5−ζ7ζ13−ζ23ζ5−ζ7ζ13−ζ230000000000000000
χ5166-6-6-300-333−3333−3333000000002-200-1-11122−2−2−2−222−33−33ζ13−ζ23ζ5−ζ7ζ13−ζ23ζ5−ζ7−ζ13+ζ23−ζ5+ζ7−ζ13+ζ23−ζ5+ζ7−ζ5+ζ7−ζ13+ζ23−ζ5+ζ7−ζ13+ζ23ζ5−ζ7ζ13−ζ23ζ5−ζ7ζ13−ζ230000000000000000
χ5266-6-6-300-333−3333−3333000000002-200-1-111−2−22222−2−2−33−33−ζ13+ζ23−ζ5+ζ7−ζ13+ζ23−ζ5+ζ7ζ13−ζ23ζ5−ζ7ζ13−ζ23ζ5−ζ7ζ5−ζ7ζ13−ζ23ζ5−ζ7ζ13−ζ23−ζ5+ζ7−ζ13+ζ23−ζ5+ζ7−ζ13+ζ230000000000000000
χ5366-6-6-300-333−3333−333300000000-220011-1-122−2−222−2−23−33−3ζ5−ζ7ζ13−ζ23ζ5−ζ7ζ13−ζ23−ζ5+ζ7−ζ13+ζ23−ζ5+ζ7−ζ13+ζ23ζ13−ζ23ζ5−ζ7ζ13−ζ23ζ5−ζ7−ζ13+ζ23−ζ5+ζ7−ζ13+ζ23−ζ5+ζ70000000000000000
χ5466-6-6-300-333−3333−333300000000-220011-1-1−2−222−2−2223−33−3−ζ5+ζ7−ζ13+ζ23−ζ5+ζ7−ζ13+ζ23ζ5−ζ7ζ13−ζ23ζ5−ζ7ζ13−ζ23−ζ13+ζ23−ζ5+ζ7−ζ13+ζ23−ζ5+ζ7ζ13−ζ23ζ5−ζ7ζ13−ζ23ζ5−ζ70000000000000000
χ556-66-6-36i−6i3-33−3i−3i3i3i000000000000−i3i3−i3i32−22−2−i2i2−i2i23−3−33ζ13−ζ23ζ5−ζ7−ζ13+ζ23−ζ5+ζ7ζ13−ζ23ζ5−ζ7−ζ13+ζ23−ζ5+ζ7ζ5+ζ7ζ13+ζ23−ζ5−ζ7−ζ13−ζ23ζ5+ζ7ζ13+ζ23−ζ5−ζ7−ζ13−ζ230000000000000000
χ566-66-6-36i−6i3-33−3i−3i3i3i000000000000−i3i3−i3i3−22−22i2−i2i2−i23−3−33−ζ13+ζ23−ζ5+ζ7ζ13−ζ23ζ5−ζ7−ζ13+ζ23−ζ5+ζ7ζ13−ζ23ζ5−ζ7−ζ5−ζ7−ζ13−ζ23ζ5+ζ7ζ13+ζ23−ζ5−ζ7−ζ13−ζ23ζ5+ζ7ζ13+ζ230000000000000000
χ576-66-6-36i−6i3-33−3i−3i3i3i000000000000i3−i3i3−i32−22−2−i2i2−i2i2−333−3ζ5−ζ7ζ13−ζ23−ζ5+ζ7−ζ13+ζ23ζ5−ζ7ζ13−ζ23−ζ5+ζ7−ζ13+ζ23ζ13+ζ23ζ5+ζ7−ζ13−ζ23−ζ5−ζ7ζ13+ζ23ζ5+ζ7−ζ13−ζ23−ζ5−ζ70000000000000000
χ586-66-6-36i−6i3-33−3i−3i3i3i000000000000i3−i3i3−i3−22−22i2−i2i2−i2−333−3−ζ5+ζ7−ζ13+ζ23ζ5−ζ7ζ13−ζ23−ζ5+ζ7−ζ13+ζ23ζ5−ζ7ζ13−ζ23−ζ13−ζ23−ζ5−ζ7ζ13+ζ23ζ5+ζ7−ζ13−ζ23−ζ5−ζ7ζ13+ζ23ζ5+ζ70000000000000000
χ596-66-6-3−6i6i3-333i3i−3i−3i000000000000−i3i3−i3i32−22−2i2−i2i2−i2−333−3ζ5−ζ7ζ13−ζ23−ζ5+ζ7−ζ13+ζ23ζ5−ζ7ζ13−ζ23−ζ5+ζ7−ζ13+ζ23−ζ13−ζ23−ζ5−ζ7ζ13+ζ23ζ5+ζ7−ζ13−ζ23−ζ5−ζ7ζ13+ζ23ζ5+ζ70000000000000000
χ606-66-6-3−6i6i3-333i3i−3i−3i000000000000−i3i3−i3i3−22−22−i2i2−i2i2−333−3−ζ5+ζ7−ζ13+ζ23ζ5−ζ7ζ13−ζ23−ζ5+ζ7−ζ13+ζ23ζ5−ζ7ζ13−ζ23ζ13+ζ23ζ5+ζ7−ζ13−ζ23−ζ5−ζ7ζ13+ζ23ζ5+ζ7−ζ13−ζ23−ζ5−ζ70000000000000000
χ616-66-6-3−6i6i3-333i3i−3i−3i000000000000i3−i3i3−i32−22−2i2−i2i2−i23−3−33ζ13−ζ23ζ5−ζ7−ζ13+ζ23−ζ5+ζ7ζ13−ζ23ζ5−ζ7−ζ13+ζ23−ζ5+ζ7−ζ5−ζ7−ζ13−ζ23ζ5+ζ7ζ13+ζ23−ζ5−ζ7−ζ13−ζ23ζ5+ζ7ζ13+ζ230000000000000000
χ626-66-6-3−6i6i3-333i3i−3i−3i000000000000i3−i3i3−i3−22−22−i2i2−i2i23−3−33−ζ13+ζ23−ζ5+ζ7ζ13−ζ23ζ5−ζ7−ζ13+ζ23−ζ5+ζ7ζ13−ζ23ζ5−ζ7ζ5+ζ7ζ13+ζ23−ζ5−ζ7−ζ13−ζ23ζ5+ζ7ζ13+ζ23−ζ5−ζ7−ζ13−ζ230000000000000000
χ636-6-66-30033-3−3i33i33i3−3i300000000002-2−i3i3i3−i32-2-220000-1-111-1-11111-1-1i3−i3−i3i3−i3i3i3−i30000000000000000
χ646-6-66-30033-3−3i33i33i3−3i300000000002-2−i3i3i3−i3-222-20000-1-11111-1-1-1-111−i3i3i3−i3i3−i3−i3i30000000000000000
χ656-6-66-30033-3−3i33i33i3−3i30000000000-22i3−i3−i3i300002i−2i−2i2i11-1-1−333−33−3−33−i−iiiii−i−i0000000000000000
χ666-6-66-30033-3−3i33i33i3−3i30000000000-22i3−i3−i3i30000−2i2i2i−2i11-1-13−3−33−333−3ii−i−i−i−iii0000000000000000
χ676-6-66-30033-33i3−3i3−3i33i300000000002-2i3−i3−i3i32-2-220000-1-111-1-11111-1-1−i3i3i3−i3i3−i3−i3i30000000000000000
χ686-6-66-30033-33i3−3i3−3i33i300000000002-2i3−i3−i3i3-222-20000-1-11111-1-1-1-111i3−i3−i3i3−i3i3i3−i30000000000000000
χ696-6-66-30033-33i3−3i3−3i33i30000000000-22−i3i3i3−i300002i−2i−2i2i11-1-13−3−33−333−3−i−iiiii−i−i0000000000000000
χ706-6-66-30033-33i3−3i3−3i33i30000000000-22−i3i3i3−i30000−2i2i2i−2i11-1-1−333−33−3−33ii−i−i−i−iii0000000000000000
χ7188-8-88008-8-800002-42-4-24-240000000000000000000000000000000000000000000000000000
χ7288-8-88008-8-80000-42-424-24-20000000000000000000000000000000000000000000000000000
χ738-8-88800-8-8800002-4-24-242-40000000000000000000000000000000000000000000000000000
χ748-8-88800-8-880000-424-24-2-420000000000000000000000000000000000000000000000000000

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