Finite Group Databasebeta

← Group #72341887

Character table — Group #72341887

Order 1536.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size111122222266666666666612121212121212121212121212123232323232323232323232323232323248484848484848484848484848484848
order12224488882222224444442244888888888836661212121224242424242424242244444488888888
χ111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-111-1-11111-1-1-1-1
χ4111111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-11111
χ51-11-11-1ii−i−i11-1-11-11-111-1-11-11-1iiiii−i−i−i−i−i1-1-1111-1-1iiii−i−i−i−i1-1i−i1-1i−i11-1-1ii−i−i
χ61-11-11-1ii−i−i11-1-11-11-111-1-11-11-1iiiii−i−i−i−i−i1-1-1111-1-1iiii−i−i−i−i-11−ii-11−ii-1-111−i−iii
χ71-11-11-1−i−iii11-1-11-11-111-1-11-11-1−i−i−i−i−iiiiii1-1-1111-1-1−i−i−i−iiiii1-1−ii1-1−ii11-1-1−i−iii
χ81-11-11-1−i−iii11-1-11-11-111-1-11-11-1−i−i−i−i−iiiiii1-1-1111-1-1−i−i−i−iiiii-11i−i-11i−i-1-111ii−i−i
χ9222222222222222222222222222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000000000000000
χ10222222-2-2-2-22222222222222222-2-2-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-1111111110000000000000000
χ112222-2-20000-2-2-2-222-2-2222222-2-200000000002222-2-2-2-2000000000000000000000000
χ122222-2-20000-2-2-2-222-2-2222222-2-20000000000-1-1-1-1111133−3−333−3−30000000000000000
χ132222-2-20000-2-2-2-222-2-2222222-2-20000000000-1-1-1-11111−3−333−3−3330000000000000000
χ142-22-22-22i2i−2i−2i22-2-22-22-222-2-22-22-22i2i2i2i2i−2i−2i−2i−2i−2i-111-1-1-111−i−i−i−iiiii0000000000000000
χ152-22-22-2−2i−2i2i2i22-2-22-22-222-2-22-22-2−2i−2i−2i−2i−2i2i2i2i2i2i-111-1-1-111iiii−i−i−i−i0000000000000000
χ162-22-2-220000-2-2222-2-2222-2-22-2-2200000000002-2-22-2-222000000000000000000000000
χ172-22-2-220000-2-2222-2-2222-2-22-2-220000000000-111-111-1-1−i3−i3i3i3i3i3−i3−i30000000000000000
χ182-22-2-220000-2-2222-2-2222-2-22-2-220000000000-111-111-1-1i3i3−i3−i3−i3−i3i3i30000000000000000
χ1933333333333-13-1-1-1-1-13-13-1-1-1-1-13-1-1-1-13-1-1-1-100000000000000001111-1-1-1-11-11-11-11-1
χ2033333333333-13-1-1-1-1-13-13-1-1-1-1-13-1-1-1-13-1-1-1-10000000000000000-1-1-1-11111-11-11-11-11
χ213333333333-13-13-1-1-1-1-13-13-1-1-1-1-13-1-1-1-13-1-1-100000000000000001111-1-1-1-1-11-11-11-11
χ223333333333-13-13-1-1-1-1-13-13-1-1-1-1-13-1-1-1-13-1-1-10000000000000000-1-1-1-111111-11-11-11-1
χ233333333333-1-1-1-13333-1-1-1-1-1-1-1-1-1-13-1-1-1-13-1-1000000000000000011111111-1-1-1-1-1-1-1-1
χ243333333333-1-1-1-13333-1-1-1-1-1-1-1-1-1-13-1-1-1-13-1-10000000000000000-1-1-1-1-1-1-1-111111111
χ25333333-3-3-3-33-13-1-1-1-1-13-13-1-1-1-1-1-31111-31111000000000000000011-1-1-1-1111-11-1-11-11
χ26333333-3-3-3-33-13-1-1-1-1-13-13-1-1-1-1-1-31111-311110000000000000000-1-11111-1-1-11-111-11-1
χ27333333-3-3-3-3-13-13-1-1-1-1-13-13-1-1-1-11-31111-3111000000000000000011-1-1-1-111-11-111-11-1
χ28333333-3-3-3-3-13-13-1-1-1-1-13-13-1-1-1-11-31111-31110000000000000000-1-11111-1-11-11-1-11-11
χ29333333-3-3-3-3-1-1-1-13333-1-1-1-1-1-1-1-111-31111-311000000000000000011-1-111-1-1-1-1-1-11111
χ30333333-3-3-3-3-1-1-1-13333-1-1-1-1-1-1-1-111-31111-3110000000000000000-1-111-1-1111111-1-1-1-1
χ313-33-33-33i3i−3i−3i3-1-31-11-113-1-31-11-113i−i−i−i−i−3iiiii00000000000000001-1i−i-11−ii1-1-11i−i−ii
χ323-33-33-33i3i−3i−3i3-1-31-11-113-1-31-11-113i−i−i−i−i−3iiiii0000000000000000-11−ii1-1i−i-111-1−iii−i
χ333-33-33-33i3i−3i−3i-131-3-11-11-131-3-11-11−i3i−i−i−ii−3iiii00000000000000001-1i−i-11−ii-111-1−iii−i
χ343-33-33-33i3i−3i−3i-131-3-11-11-131-3-11-11−i3i−i−i−ii−3iiii0000000000000000-11−ii1-1i−i1-1-11i−i−ii
χ353-33-33-33i3i−3i−3i-1-1113-33-3-1-111-11-11−i−i3i−i−iii−3iii00000000000000001-1i−i1-1i−i-1-111−i−iii
χ363-33-33-33i3i−3i−3i-1-1113-33-3-1-111-11-11−i−i3i−i−iii−3iii0000000000000000-11−ii-11−ii11-1-1ii−i−i
χ373-33-33-3−3i−3i3i3i3-1-31-11-113-1-31-11-11−3iiiii3i−i−i−i−i00000000000000001-1−ii-11i−i1-1-11−iii−i
χ383-33-33-3−3i−3i3i3i3-1-31-11-113-1-31-11-11−3iiiii3i−i−i−i−i0000000000000000-11i−i1-1−ii-111-1i−i−ii
χ393-33-33-3−3i−3i3i3i-131-3-11-11-131-3-11-11i−3iiii−i3i−i−i−i00000000000000001-1−ii-11i−i-111-1i−i−ii
χ403-33-33-3−3i−3i3i3i-131-3-11-11-131-3-11-11i−3iiii−i3i−i−i−i0000000000000000-11i−i1-1−ii1-1-11−iii−i
χ413-33-33-3−3i−3i3i3i-1-1113-33-3-1-111-11-11ii−3iii−i−i3i−i−i00000000000000001-1−ii1-1−ii-1-111ii−i−i
χ423-33-33-3−3i−3i3i3i-1-1113-33-3-1-111-11-11ii−3iii−i−i3i−i−i0000000000000000-11i−i-11i−i11-1-1−i−iii
χ436666666666-2-2-2-2-2-2-2-2-2-2-2-22222-2-2-222-2-2-22200000000000000000000000000000000
χ44666666-6-6-6-6-2-2-2-2-2-2-2-2-2-2-2-22222222-2-2222-2-200000000000000000000000000000000
χ456666-6-60000222266-6-6-2-2-2-2-2-222000000000000000000000000000000000000000000
χ466666-6-600002222-2-222-2-2-2-222-2-20004i−4i0004i−4i00000000000000000000000000000000
χ476666-6-600002222-2-222-2-2-2-222-2-2000−4i4i000−4i4i00000000000000000000000000000000
χ486666-6-600002-62-6-2-222-26-26-2-222000000000000000000000000000000000000000000
χ496666-6-60000-62-62-2-2226-26-2-2-222000000000000000000000000000000000000000000
χ506-66-66-66i6i−6i−6i-2-222-22-22-2-2222-22-2−2i−2i−2i2i2i2i2i2i−2i−2i00000000000000000000000000000000
χ516-66-66-6−6i−6i6i6i-2-222-22-22-2-2222-22-22i2i2i−2i−2i−2i−2i−2i2i2i00000000000000000000000000000000
χ526-66-6-66000022-2-26-6-66-2-222-222-2000000000000000000000000000000000000000000
χ536-66-6-66000022-2-2-222-2-2-2222-2-220004-4000-4400000000000000000000000000000000
χ546-66-6-66000022-2-2-222-2-2-2222-2-22000-440004-400000000000000000000000000000000
χ556-66-6-6600002-6-26-222-2-262-6-222-2000000000000000000000000000000000000000000
χ566-66-6-660000-626-2-222-26-2-62-222-2000000000000000000000000000000000000000000
χ5788-8-800−4i24i2−4i24i20000000000000000000000000022-2-20000−i2i2−i2i2−i2i2−i2i20000000000000000
χ5888-8-800−4i24i2−4i24i200000000000000000000000000-1-1113−33−3ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ230000000000000000
χ5988-8-800−4i24i2−4i24i200000000000000000000000000-1-111−33−33ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ70000000000000000
χ6088-8-8004i2−4i24i2−4i20000000000000000000000000022-2-20000i2−i2i2−i2i2−i2i2−i20000000000000000
χ6188-8-8004i2−4i24i2−4i200000000000000000000000000-1-1113−33−3−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ230000000000000000
χ6288-8-8004i2−4i24i2−4i200000000000000000000000000-1-111−33−33−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ70000000000000000
χ638-8-880042−42−4242000000000000000000000000002-22-200002−22−2−22−220000000000000000
χ648-8-880042−42−424200000000000000000000000000-11-113−3−33ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ70000000000000000
χ658-8-880042−42−424200000000000000000000000000-11-11−333−3ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ230000000000000000
χ668-8-8800−424242−42000000000000000000000000002-22-20000−22−222−22−20000000000000000
χ678-8-8800−424242−4200000000000000000000000000-11-113−3−33−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ70000000000000000
χ688-8-8800−424242−4200000000000000000000000000-11-11−333−3−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ230000000000000000

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