Finite Group Databasebeta

← Group #72252558

Character table — Group #72252558

Order 3072.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70
size11244466881212121212121212121212161616161616242424242424242424242424242432323232326464646464646464646496969696128128128128128128128128128128
order1222242288222222444442233662244888888888844466666666661212444412121212121224242424
χ11111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111−1−i32−1+i32−1−i32−1+i3211111111111111111−1−i32−1+i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1−i32−1+i32−1−i32−1+i321111−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32
χ311111111111111111111111−1+i32−1−i32−1+i32−1−i3211111111111111111−1+i32−1−i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1+i32−1−i32−1+i32−1−i321111−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32
χ4111111111111111111111-1-1111111111111111111-1-1-1111-1-11-1-11111-1-1-1-1-1-1-1-1-1-11111
χ5111111111111111111111-1-1−1−i32−1+i32−1−i32−1+i3211111111111111-1-1-1−1−i32−1+i32−1−i321+i321+i32−1+i321−i321−i32−1−i32−1+i32−1−i32−1+i32-1-1-1-11+i321−i321+i321+i321−i321−i32−1−i32−1−i32−1+i32−1+i32
χ6111111111111111111111-1-1−1+i32−1−i32−1+i32−1−i3211111111111111-1-1-1−1+i32−1−i32−1+i321−i321−i32−1−i321+i321+i32−1+i32−1−i32−1+i32−1−i32-1-1-1-11−i321+i321−i321−i321+i321+i32−1+i32−1+i32−1−i32−1−i32
χ711111111-1-1111111111111111111111-1-1-1-1-1-1-1-1-1-11-1-111111111111111-1-111-1-1-1-1-1-1-1-1
χ811111111-1-11111111111111−1−i32−1+i32−1−i32−1+i321111-1-1-1-1-1-1-1-1-1-11-1-1−1−i32−1+i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1−i32−1+i32−1−i32−1+i3211-1-1−1−i32−1+i321+i321+i321−i321−i321+i321+i321−i321−i32
χ911111111-1-11111111111111−1+i32−1−i32−1+i32−1−i321111-1-1-1-1-1-1-1-1-1-11-1-1−1+i32−1−i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1+i32−1−i32−1+i32−1−i3211-1-1−1+i32−1−i321−i321−i321+i321+i321−i321−i321+i321+i32
χ1011111111-1-111111111111-1-111111111-1-1-1-1-1-1-1-1-1-1-111111-1-11-1-11111-1-111-1-11111-1-1-1-1
χ1111111111-1-111111111111-1-1−1−i32−1+i32−1−i32−1+i321111-1-1-1-1-1-1-1-1-1-1-111−1−i32−1+i32−1−i321+i321+i32−1+i321−i321−i32−1−i32−1+i32−1−i32−1+i32-1-1111+i321−i32−1−i32−1−i32−1+i32−1+i321+i321+i321−i321−i32
χ1211111111-1-111111111111-1-1−1+i32−1−i32−1+i32−1−i321111-1-1-1-1-1-1-1-1-1-1-111−1+i32−1−i32−1+i321−i321−i32−1−i321+i321+i32−1+i32−1−i32−1+i32−1−i32-1-1111−i321+i32−1+i32−1+i32−1−i32−1−i321−i321−i321+i321+i32
χ131111-1-111i−i111-1-1-111-1-1-11111111-11-1iiiii−i−i−i−i−i-1i−i11111111-1-1-1-11-1i−i-1-1i−ii−ii−ii−i
χ141111-1-111i−i111-1-1-111-1-1-111−1−i32−1+i32−1−i32−1+i321-11-1iiiii−i−i−i−i−i-1i−i−1−i32−1+i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i321+i321−i321+i321−i321-1i−i1+i321−i32ζ11−ζ11ζ7−ζ7ζ11−ζ11ζ7−ζ7
χ151111-1-111i−i111-1-1-111-1-1-111−1+i32−1−i32−1+i32−1−i321-11-1iiiii−i−i−i−i−i-1i−i−1+i32−1−i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i321−i321+i321−i321+i321-1i−i1−i321+i32ζ7−ζ7ζ11−ζ11ζ7−ζ7ζ11−ζ11
χ161111-1-111i−i111-1-1-111-1-1-1-1-111111-11-1iiiii−i−i−i−i−i1−ii111-1-11-1-1-1-1-1-1-11−ii11−ii−iii−ii−i
χ171111-1-111i−i111-1-1-111-1-1-1-1-1−1−i32−1+i32−1−i32−1+i321-11-1iiiii−i−i−i−i−i1−ii−1−i32−1+i32−1−i321+i321+i32−1+i321−i321−i321+i321−i321+i321−i32-11−ii−1−i32−1+i32−ζ11ζ11−ζ7ζ7ζ11−ζ11ζ7−ζ7
χ181111-1-111i−i111-1-1-111-1-1-1-1-1−1+i32−1−i32−1+i32−1−i321-11-1iiiii−i−i−i−i−i1−ii−1+i32−1−i32−1+i321−i321−i32−1−i321+i321+i321−i321+i321−i321+i32-11−ii−1+i32−1−i32−ζ7ζ7−ζ11ζ11ζ7−ζ7ζ11−ζ11
χ191111-1-111−ii111-1-1-111-1-1-11111111-11-1−i−i−i−i−iiiiii-1−ii11111111-1-1-1-11-1−ii-1-1−ii−ii−ii−ii
χ201111-1-111−ii111-1-1-111-1-1-111−1−i32−1+i32−1−i32−1+i321-11-1−i−i−i−i−iiiiii-1−ii−1−i32−1+i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i321+i321−i321+i321−i321-1−ii1+i321−i32−ζ11ζ11−ζ7ζ7−ζ11ζ11−ζ7ζ7
χ211111-1-111−ii111-1-1-111-1-1-111−1+i32−1−i32−1+i32−1−i321-11-1−i−i−i−i−iiiiii-1−ii−1+i32−1−i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i321−i321+i321−i321+i321-1−ii1−i321+i32−ζ7ζ7−ζ11ζ11−ζ7ζ7−ζ11ζ11
χ221111-1-111−ii111-1-1-111-1-1-1-1-111111-11-1−i−i−i−i−iiiiii1i−i111-1-11-1-1-1-1-1-1-11i−i11i−ii−i−ii−ii
χ231111-1-111−ii111-1-1-111-1-1-1-1-1−1−i32−1+i32−1−i32−1+i321-11-1−i−i−i−i−iiiiii1i−i−1−i32−1+i32−1−i321+i321+i32−1+i321−i321−i321+i321−i321+i321−i32-11i−i−1−i32−1+i32ζ11−ζ11ζ7−ζ7−ζ11ζ11−ζ7ζ7
χ241111-1-111−ii111-1-1-111-1-1-1-1-1−1+i32−1−i32−1+i32−1−i321-11-1−i−i−i−i−iiiiii1i−i−1+i32−1−i32−1+i321−i321−i32−1−i321+i321+i321−i321+i321−i321+i32-11i−i−1+i32−1−i32ζ7−ζ7ζ11−ζ11−ζ7ζ7−ζ11ζ11
χ25222-22-2220022-2-2-2222-2-2-2002222-22-22000000000000022-200-20022-2-200000000000000
χ26222-22-2220022-2-2-2222-2-2-200−1−i3−1+i3−1−i3−1+i3-22-220000000000000−1−i3−1+i31+i3001−i300−1−i3−1+i31+i31−i300000000000000
χ27222-22-2220022-2-2-2222-2-2-200−1+i3−1−i3−1+i3−1−i3-22-220000000000000−1+i3−1−i31−i3001+i300−1+i3−1−i31−i31+i300000000000000
χ28222-2-22220022-222-222222002222-2-2-2-2000000000000022-200-200-2-22200000000000000
χ29222-2-22220022-222-22222200−1−i3−1+i3−1−i3−1+i3-2-2-2-20000000000000−1−i3−1+i31+i3001−i3001+i31−i3−1−i3−1+i300000000000000
χ30222-2-22220022-222-22222200−1+i3−1−i3−1+i3−1−i3-2-2-2-20000000000000−1+i3−1−i31−i3001+i3001−i31+i3−1+i3−1−i300000000000000
χ313333333333-1-13-1-13-1-13-1-1330000-1-1-1-13-1-1-1-13-1-1-1-1333000000000000-1-1-1-10000000000
χ323333333333-1-13-1-13-1-13-1-1-3-30000-1-1-1-13-1-1-1-13-1-1-1-1-3-3-300000000000011110000000000
χ3333333333-3-3-1-13-1-13-1-13-1-1330000-1-1-1-1-31111-311113-3-3000000000000-1-1110000000000
χ3433333333-3-3-1-13-1-13-1-13-1-1-3-30000-1-1-1-1-31111-31111-33300000000000011-1-10000000000
χ353333-3-3333i−3i-1-1311-3-1-1-311330000-11-113i−i−i−i−i−3iiiii-33i−3i000000000000-11−ii0000000000
χ363333-3-3333i−3i-1-1311-3-1-1-311-3-30000-11-113i−i−i−i−i−3iiiii3−3i3i0000000000001-1i−i0000000000
χ373333-3-333−3i3i-1-1311-3-1-1-311330000-11-11−3iiiii3i−i−i−i−i-3−3i3i000000000000-11i−i0000000000
χ383333-3-333−3i3i-1-1311-3-1-1-311-3-30000-11-11−3iiiii3i−i−i−i−i33i−3i0000000000001-1−ii0000000000
χ3944-40004-4004-400004-400000444400000000000000000-4-4000000000000000000000000
χ4044-40004-4004-400004-400000−2−2i3−2+2i3−2−2i3−2+2i3000000000000000002+2i32−2i3000000000000000000000000
χ4144-40004-4004-400004-400000−2+2i3−2−2i3−2+2i3−2−2i3000000000000000002−2i32+2i3000000000000000000000000
χ42666666-2-26622-2-2-2-2-2-2-22200000022-2-2-222-2-2-222-2-200000000000000000000000000000
χ43666666-2-266-2-2-222-222-2-2-2000000-2-222-2-2-222-2-2-22200000000000000000000000000000
χ44666666-2-2-6-622-2-2-2-2-2-2-22200000022-2-22-2-2222-2-22200000000000000000000000000000
χ45666666-2-2-6-6-2-2-222-222-2-2-2000000-2-222222-2-2222-2-200000000000000000000000000000
χ466666-6-6-2-26i−6i22-2222-2-22-2-20000002-2-22−2i2i2i−2i−2i2i−2i−2i2i2i00000000000000000000000000000
χ476666-6-6-2-26i−6i-2-2-2-2-2222222000000-222-2−2i−2i−2i2i2i2i2i2i−2i−2i00000000000000000000000000000
χ486666-6-6-2-2−6i6i22-2222-2-22-2-20000002-2-222i−2i−2i2i2i−2i2i2i−2i−2i00000000000000000000000000000
χ496666-6-6-2-2−6i6i-2-2-2-2-2222222000000-222-22i2i2i−2i−2i−2i−2i−2i2i2i00000000000000000000000000000
χ50666-66-66600-2-2-6226-2-2-6220000002-22-2000000000000000000000000000000000000000
χ51666-66-6-2-20022222-2-2-22-2-2000000-222-204i−4i0004i−4i0000000000000000000000000000000
χ52666-66-6-2-20022222-2-2-22-2-2000000-222-20−4i4i000−4i4i0000000000000000000000000000000
χ53666-66-6-2-200-2-22-2-2-2222220000002-2-220004i−4i0004i−4i00000000000000000000000000000
χ54666-66-6-2-200-2-22-2-2-2222220000002-2-22000−4i4i000−4i4i00000000000000000000000000000
χ55666-6-666600-2-2-6-2-2-6-2-26-2-20000002222000000000000000000000000000000000000000
χ56666-6-66-2-200222-2-22-2-2-222000000-2-22204-4000-440000000000000000000000000000000
χ57666-6-66-2-200222-2-22-2-2-222000000-2-2220-440004-40000000000000000000000000000000
χ58666-6-66-2-200-2-2222222-2-2-200000022-2-20004-4000-4400000000000000000000000000000
χ59666-6-66-2-200-2-2222222-2-2-200000022-2-2000-440004-400000000000000000000000000000
χ601212-1200012-1200-440000-440000000000000000000000000000000000000000000000000000
χ611212-12000-44004-40000-4408-80000000000000000000000000000000000000000000000000
χ621212-12000-44004-40000-440-880000000000000000000000000000000000000000000000000
χ631212-12000-4400-4408-804-40000000000000000000000000000000000000000000000000000
χ641212-12000-4400-440-8804-40000000000000000000000000000000000000000000000000000
χ6516-1600000000000000000004-444-4-4000000000000000000002-202-2000000000000000000
χ6616-1600000000000000000004-4−2−2i3−2+2i32+2i32−2i300000000000000000000−1−i31+i30−1+i31−i3000000000000000000
χ6716-1600000000000000000004-4−2+2i3−2−2i32−2i32+2i300000000000000000000−1+i31−i30−1−i31+i3000000000000000000
χ6816-160000000000000000000-4444-4-400000000000000000000-220-22000000000000000000
χ6916-160000000000000000000-44−2−2i3−2+2i32+2i32−2i3000000000000000000001+i3−1−i301−i3−1+i3000000000000000000
χ7016-160000000000000000000-44−2+2i3−2−2i32−2i32+2i3000000000000000000001−i3−1+i301+i3−1−i3000000000000000000

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