Finite Group Databasebeta

← Group #13052101

Character table — Group #13052101

Order 1344.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59
size1122244667777881212121414141414142424242424242828282828282828282828282828282828282828282856565656565656
order12244247143366281428286612121212141414285656244444666612121212121212121212121266824242424
χ111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111-1-1-1-1-1-111-1-111-1-1-1-1-1-1-1-1-1-111-111-1-1
χ31111111111111-1-11111111111-1-11-1-11111-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1
χ41111111111111-1-11111111111-1-11-1-1-1-1-1-11111-1-111-1-1-1-1-1-11111-1-11-1-111
χ5111111111−1−i32−1+i32−1−i32−1+i3211111−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32111111111111−1−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+i32−1−i32−1+i321−1−i32−1+i32−1−i32−1+i32
χ6111111111−1−i32−1+i32−1−i32−1+i3211111−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32111111-1-1-1-1-1-1−1−i32−1+i321+i321−i32−1−i32−1+i321+i321+i321+i321−i321−i321−i321+i321+i321−i321−i32−1−i32−1+i32-1−1−i32−1+i321+i321−i32
χ7111111111−1−i32−1+i32−1−i32−1+i32-1-1111−1−i32−1+i32−1−i32−1−i32−1+i32−1+i321-1-11-1-11111-1-1−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i321+i321+i321−i321−i321+i321−i32-11+i321−i321+i321−i32
χ8111111111−1−i32−1+i32−1−i32−1+i32-1-1111−1−i32−1+i32−1−i32−1−i32−1+i32−1+i321-1-11-1-1-1-1-1-111−1−i32−1+i321+i321−i32−1−i32−1+i321+i321+i321+i321−i321−i321−i32−1−i32−1−i32−1+i32−1+i321+i321−i3211+i321−i32−1−i32−1+i32
χ9111111111−1+i32−1−i32−1+i32−1−i3211111−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32111111111111−1+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−i32−1+i32−1−i321−1+i32−1−i32−1+i32−1−i32
χ10111111111−1+i32−1−i32−1+i32−1−i3211111−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32111111-1-1-1-1-1-1−1+i32−1−i321−i321+i32−1+i32−1−i321−i321−i321−i321+i321+i321+i321−i321−i321+i321+i32−1+i32−1−i32-1−1+i32−1−i321−i321+i32
χ11111111111−1+i32−1−i32−1+i32−1−i32-1-1111−1+i32−1−i32−1+i32−1+i32−1−i32−1−i321-1-11-1-11111-1-1−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i321−i321−i321+i321+i321−i321+i32-11−i321+i321−i321+i32
χ12111111111−1+i32−1−i32−1+i32−1−i32-1-1111−1+i32−1−i32−1+i32−1+i32−1−i32−1−i321-1-11-1-1-1-1-1-111−1+i32−1−i321−i321+i32−1+i32−1−i321−i321−i321−i321+i321+i321+i32−1+i32−1+i32−1−i32−1−i321−i321+i3211−i321+i32−1+i32−1−i32
χ1311111-1-11111111-1111111111-111-1-1-111-1-1-1-1-1-111-1-11-1-11-1-1-1-1-1-1111-1-111
χ1411111-1-11111111-1111111111-111-1-1-1-1-11111-1-1-1-1-1-1-111-111111111-1-1-1-1-1
χ1511111-1-1111111-11111111111-1-1-1-11111-1-111-1-111-1-11-1-11-1-11111-1-1-111-1-1
χ1611111-1-1111111-11111111111-1-1-1-111-1-111-1-1-1-1-1-1-1-1-111-111-1-1-1-1-1-111111
χ1711111-1-111−1−i32−1+i32−1−i32−1+i321-1111−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32-111-1-1-111-1-1-1-11+i321−i32−1−i32−1+i321+i321−i32−1−i321+i321+i32−1+i321−i321−i321+i321+i321−i321−i32−1−i32−1+i3211+i321−i32−1−i32−1+i32
χ1811111-1-111−1−i32−1+i32−1−i32−1+i321-1111−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32-111-1-1-1-1-111111+i321−i321+i321−i321+i321−i321+i32−1−i32−1−i321−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1+i32-11+i321−i321+i321−i32
χ1911111-1-111−1−i32−1+i32−1−i32−1+i32-11111−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32-1-1-1-11111-1-1111+i321−i32−1−i32−1+i321+i321−i32−1−i321+i321+i32−1+i321−i321−i32−1−i32−1−i32−1+i32−1+i321+i321−i32-1−1−i32−1+i321+i321−i32
χ2011111-1-111−1−i32−1+i32−1−i32−1+i32-11111−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32-1-1-1-111-1-111-1-11+i321−i321+i321−i321+i321−i321+i32−1−i32−1−i321−i32−1+i32−1+i321+i321+i321−i321−i321+i321−i321−1−i32−1+i32−1−i32−1+i32
χ2111111-1-111−1+i32−1−i32−1+i32−1−i321-1111−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32-111-1-1-111-1-1-1-11−i321+i32−1+i32−1−i321−i321+i32−1+i321−i321−i32−1−i321+i321+i321−i321−i321+i321+i32−1+i32−1−i3211−i321+i32−1+i32−1−i32
χ2211111-1-111−1+i32−1−i32−1+i32−1−i321-1111−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32-111-1-1-1-1-111111−i321+i321−i321+i321−i321+i321−i32−1+i32−1+i321+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1−i32-11−i321+i321−i321+i32
χ2311111-1-111−1+i32−1−i32−1+i32−1−i32-11111−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32-1-1-1-11111-1-1111−i321+i32−1+i32−1−i321−i321+i32−1+i321−i321−i32−1−i321+i321+i32−1+i32−1+i32−1−i32−1−i321−i321+i32-1−1+i32−1−i321−i321+i32
χ2411111-1-111−1+i32−1−i32−1+i32−1−i32-11111−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32-1-1-1-111-1-111-1-11−i321+i321−i321+i321−i321+i321−i32−1+i32−1+i321+i32−1−i32−1−i321−i321−i321+i321+i321−i321+i321−1+i32−1−i32−1+i32−1−i32
χ25222-2-200222222002-2-222-2-2-2-2000000002-20000000002-202-200000000000
χ26222-2-200222222002-2-222-2-2-2-200000000-22000000000-220-2200000000000
χ27222-2-20022−1−i3−1+i3−1−i3−1+i3002-2-2−1−i3−1+i31+i31+i31−i31−i3000000002-2000000000−1−i31+i30−1+i31−i300000000000
χ28222-2-20022−1−i3−1+i3−1−i3−1+i3002-2-2−1−i3−1+i31+i31+i31−i31−i300000000-220000000001+i3−1−i301−i3−1+i300000000000
χ29222-2-20022−1+i3−1−i3−1+i3−1−i3002-2-2−1+i3−1−i31−i31−i31+i31+i3000000002-2000000000−1+i31−i30−1−i31+i300000000000
χ30222-2-20022−1+i3−1−i3−1+i3−1−i3002-2-2−1+i3−1−i31−i31−i31+i31+i300000000-220000000001−i3−1+i301+i3−1−i300000000000
χ3122-22-22-222222200-2-22-2-22-22-2200-2000000002200-2-200000000000000000
χ3222-22-22-222−1−i3−1+i3−1−i3−1+i300-2-221+i31−i3−1−i31+i3−1+i31−i3200-200000000−1−i3−1+i3001+i31−i300000000000000000
χ3322-22-22-222−1+i3−1−i3−1+i3−1−i300-2-221−i31+i3−1+i31−i3−1−i31+i3200-200000000−1+i3−1−i3001−i31+i300000000000000000
χ3422-22-2-2222222200-2-22-2-22-22-2-200200000000-2-2002200000000000000000
χ3522-22-2-2222−1−i3−1+i3−1−i3−1+i300-2-221+i31−i3−1−i31+i3−1+i31−i3-2002000000001+i31−i300−1−i3−1+i300000000000000000
χ3622-22-2-2222−1+i3−1−i3−1+i3−1−i300-2-221−i31+i3−1+i31−i3−1−i31+i3-2002000000001−i31+i300−1+i3−1−i300000000000000000
χ3722-2-220022222200-22-2-2-2-22-220000002-20000002200-200-20000000000000
χ3822-2-220022222200-22-2-2-2-22-22000000-22000000-2-20020020000000000000
χ3922-2-220022−1−i3−1+i3−1−i3−1+i300-22-21+i31−i31+i3−1−i31−i3−1+i30000002-2000000−1−i3−1+i3001+i3001−i30000000000000
χ4022-2-220022−1−i3−1+i3−1−i3−1+i300-22-21+i31−i31+i3−1−i31−i3−1+i3000000-220000001+i31−i300−1−i300−1+i30000000000000
χ4122-2-220022−1+i3−1−i3−1+i3−1−i300-22-21−i31+i31−i3−1+i31+i3−1−i30000002-2000000−1+i3−1−i3001−i3001+i30000000000000
χ4222-2-220022−1+i3−1−i3−1+i3−1−i300-22-21−i31+i31−i3−1+i31+i3−1−i3000000-220000001−i31+i300−1+i300−1−i30000000000000
χ434-4000004-444-4-40000000000000000000002i−2i0000000000002i−2i2i−2i0000000
χ444-4000004-444-4-4000000000000000000000−2i2i000000000000−2i2i−2i2i0000000
χ454-4000004-4−2−2i3−2+2i32+2i32−2i30000000000000000000002i−2i0000000000002ζ11+2ζ23+2ζ47+2ζ59+2ζ71+2ζ83−2ζ11−2ζ23−2ζ47−2ζ59−2ζ71−2ζ832ζ19+2ζ31+2ζ43+2ζ55+2ζ67+2ζ79−2ζ19−2ζ31−2ζ43−2ζ55−2ζ67−2ζ790000000
χ464-4000004-4−2−2i3−2+2i32+2i32−2i3000000000000000000000−2i2i000000000000−2ζ11−2ζ23−2ζ47−2ζ59−2ζ71−2ζ832ζ11+2ζ23+2ζ47+2ζ59+2ζ71+2ζ83−2ζ19−2ζ31−2ζ43−2ζ55−2ζ67−2ζ792ζ19+2ζ31+2ζ43+2ζ55+2ζ67+2ζ790000000
χ474-4000004-4−2+2i3−2−2i32−2i32+2i30000000000000000000002i−2i0000000000002ζ19+2ζ31+2ζ43+2ζ55+2ζ67+2ζ79−2ζ19−2ζ31−2ζ43−2ζ55−2ζ67−2ζ792ζ11+2ζ23+2ζ47+2ζ59+2ζ71+2ζ83−2ζ11−2ζ23−2ζ47−2ζ59−2ζ71−2ζ830000000
χ484-4000004-4−2+2i3−2−2i32−2i32+2i3000000000000000000000−2i2i000000000000−2ζ19−2ζ31−2ζ43−2ζ55−2ζ67−2ζ792ζ19+2ζ31+2ζ43+2ζ55+2ζ67+2ζ79−2ζ11−2ζ23−2ζ47−2ζ59−2ζ71−2ζ832ζ11+2ζ23+2ζ47+2ζ59+2ζ71+2ζ830000000
χ496666666-1-1000066-1-1-1000000-1-1-1-1-1-100000000000000000000000000000
χ506666666-1-10000-6-6-1-1-1000000-111-11100000000000000000000000000000
χ5166666-6-6-1-100006-6-1-1-10000001-1-111100000000000000000000000000000
χ5266666-6-6-1-10000-66-1-1-10000001111-1-100000000000000000000000000000
χ5366-66-66-6-1-100000011-1000000-1−i7i71−i7i700000000000000000000000000000
χ5466-66-66-6-1-100000011-1000000-1i7−i71i7−i700000000000000000000000000000
χ5566-66-6-66-1-100000011-10000001−i7i7-1i7−i700000000000000000000000000000
χ5666-66-6-66-1-100000011-10000001i7−i7-1−i7i700000000000000000000000000000
χ57121212-12-1200-2-2000000-22200000000000000000000000000000000000000000
χ581212-12-121200-2-20000002-2200000000000000000000000000000000000000000
χ5924-2400000-4400000000000000000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 84 (ζ84 = 1); i = ζ21.