Finite Group Databasebeta

← Group #11710382

Character table — Group #11710382

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62
size112222244444444466668888888888888812121212121216161616161616161616242424243232323232323232
order12244882334668882244446688121212122424242424888866121224242424242422881212121224242424
χ111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111-1-111-1-1111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111−1−i32−1+i321−1−i32−1+i32111111111−1−i32−1+i3211−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32111111−1−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
χ411111111−1−i32−1+i321−1−i32−1+i321111111-1-1−1−i32−1+i32-1-1−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32111111−1−i32−1+i32−1−i32−1+i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32-1-1-1-11+i321+i321−i321−i321+i321+i321−i321−i32
χ511111111−1+i32−1−i321−1+i32−1−i32111111111−1+i32−1−i3211−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32111111−1+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
χ611111111−1+i32−1−i321−1+i32−1−i321111111-1-1−1+i32−1−i32-1-1−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32111111−1+i32−1−i32−1+i32−1−i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32-1-1-1-11−i321−i321+i321+i321−i321−i321+i321+i32
χ71111111-111-1111-1-111111111-1-111111111-1-111-1-1-1-1-1-11-1-11-1-111-1-11111-1-1-1-1
χ81111111-111-1111-1-11111-1-1111111111111-1-111-1-1-1-1-1-11-1-11-1-1-1-111-1-1-1-11111
χ91111111-1−1−i32−1+i32-1−1−i32−1+i321-1-1111111−1−i32−1+i32-1-1−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32-1-111-1-11+i321−i321+i321−i32−1−i321+i321+i32−1+i321−i321−i3211-1-1−1−i32−1−i32−1+i32−1+i321+i321+i321−i321−i32
χ101111111-1−1−i32−1+i32-1−1−i32−1+i321-1-11111-1-1−1−i32−1+i3211−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32-1-111-1-11+i321−i321+i321−i32−1−i321+i321+i32−1+i321−i321−i32-1-1111+i321+i321−i321−i32−1−i32−1−i32−1+i32−1+i32
χ111111111-1−1+i32−1−i32-1−1+i32−1−i321-1-1111111−1+i32−1−i32-1-1−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32-1-111-1-11−i321+i321−i321+i32−1+i321−i321−i32−1−i321+i321+i3211-1-1−1+i32−1+i32−1−i32−1−i321−i321−i321+i321+i32
χ121111111-1−1+i32−1−i32-1−1+i32−1−i321-1-11111-1-1−1+i32−1−i3211−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32-1-111-1-11−i321+i321−i321+i32−1+i321−i321−i32−1−i321+i321+i32-1-1111−i321−i321+i321+i32−1+i32−1+i32−1−i32−1−i32
χ1311111-1-1111111-1-1-111111-1111-11111-1-1-1-111-1-1-1-11111-1-1-1-1-1-11-11-11-11-11-11-1
χ1411111-1-1111111-1-1-11111-1111-111111-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-11-11-11-11-11-11
χ1511111-1-11−1−i32−1+i321−1−i32−1+i32-1-1-111111-1−1−i32−1+i321-1−1−i32−1−i32−1+i32−1+i321+i321+i321−i321−i3211-1-1-1-1−1−i32−1+i32−1−i32−1+i321+i321+i321+i321−i321−i321−i321-11-1−1−i321+i32−1+i321−i32−1−i321+i32−1+i321−i32
χ1611111-1-11−1−i32−1+i321−1−i32−1+i32-1-1-11111-11−1−i32−1+i32-11−1−i32−1−i32−1+i32−1+i321+i321+i321−i321−i3211-1-1-1-1−1−i32−1+i32−1−i32−1+i321+i321+i321+i321−i321−i321−i32-11-111+i32−1−i321−i32−1+i321+i32−1−i321−i32−1+i32
χ1711111-1-11−1+i32−1−i321−1+i32−1−i32-1-1-111111-1−1+i32−1−i321-1−1+i32−1+i32−1−i32−1−i321−i321−i321+i321+i3211-1-1-1-1−1+i32−1−i32−1+i32−1−i321−i321−i321−i321+i321+i321+i321-11-1−1+i321−i32−1−i321+i32−1+i321−i32−1−i321+i32
χ1811111-1-11−1+i32−1−i321−1+i32−1−i32-1-1-11111-11−1+i32−1−i32-11−1+i32−1+i32−1−i32−1−i321−i321−i321+i321+i3211-1-1-1-1−1+i32−1−i32−1+i32−1−i321−i321−i321−i321+i321+i321+i32-11-111−i32−1+i321+i32−1−i321−i32−1+i321+i32−1−i32
χ1911111-1-1-111-111-11111111-111-111111-1-1-1-1-1-1-1-111-1-1-1-1-111-1111-1-111-11-1-11-11
χ2011111-1-1-111-111-1111111-11111-11111-1-1-1-1-1-1-1-111-1-1-1-1-111-111-111-1-11-111-11-1
χ2111111-1-1-1−1−i32−1+i32-1−1−i32−1+i32-11111111-1−1−i32−1+i32-11−1−i32−1−i32−1+i32−1+i321+i321+i321−i321−i32-1-1-1-1111+i321−i321+i321−i321+i32−1−i32−1−i321−i32−1+i32−1+i321-1-11−1−i321+i32−1+i321−i321+i32−1−i321−i32−1+i32
χ2211111-1-1-1−1−i32−1+i32-1−1−i32−1+i32-1111111-11−1−i32−1+i321-1−1−i32−1−i32−1+i32−1+i321+i321+i321−i321−i32-1-1-1-1111+i321−i321+i321−i321+i32−1−i32−1−i321−i32−1+i32−1+i32-111-11+i32−1−i321−i32−1+i32−1−i321+i32−1+i321−i32
χ2311111-1-1-1−1+i32−1−i32-1−1+i32−1−i32-11111111-1−1+i32−1−i32-11−1+i32−1+i32−1−i32−1−i321−i321−i321+i321+i32-1-1-1-1111−i321+i321−i321+i321−i32−1+i32−1+i321+i32−1−i32−1−i321-1-11−1+i321−i32−1−i321+i321−i32−1+i321+i32−1−i32
χ2411111-1-1-1−1+i32−1−i32-1−1+i32−1−i32-1111111-11−1+i32−1−i321-1−1+i32−1+i32−1−i32−1−i321−i321−i321+i321+i32-1-1-1-1111−i321+i321−i321+i321−i32−1+i32−1+i321+i32−1−i32−1−i32-111-11−i32−1+i321+i32−1−i32−1+i321−i32−1−i321+i32
χ25222-2-20002202202i−2i-2-222002200-2-2-2-2000000002i−2i000002i−2i02i−2i000000000000
χ26222-2-2000220220−2i2i-2-222002200-2-2-2-200000000−2i2i00000−2i2i0−2i2i000000000000
χ27222-2-2000−1−i3−1+i30−1−i3−1+i302i−2i-2-22200−1−i3−1+i3001+i31+i31−i31−i3000000002i−2i000002ζ22−2ζ2202ζ14−2ζ14000000000000
χ28222-2-2000−1−i3−1+i30−1−i3−1+i30−2i2i-2-22200−1−i3−1+i3001+i31+i31−i31−i300000000−2i2i00000−2ζ222ζ220−2ζ142ζ14000000000000
χ29222-2-2000−1+i3−1−i30−1+i3−1−i302i−2i-2-22200−1+i3−1−i3001−i31−i31+i31+i3000000002i−2i000002ζ14−2ζ1402ζ22−2ζ22000000000000
χ30222-2-2000−1+i3−1−i30−1+i3−1−i30−2i2i-2-22200−1+i3−1−i3001−i31−i31+i31+i300000000−2i2i00000−2ζ142ζ140−2ζ222ζ22000000000000
χ3122-22-200222-2220002-22-200-2-2002-22-20000-22000022-2-2000000000000000000
χ3222-22-2002−1−i3−1+i3-2−1−i3−1+i30002-22-2001+i31−i300−1−i31+i3−1+i31−i30000-220000−1−i3−1+i31+i31−i3000000000000000000
χ3322-22-2002−1+i3−1−i3-2−1+i3−1−i30002-22-2001−i31+i300−1+i31−i3−1−i31+i30000-220000−1+i3−1−i31−i31+i3000000000000000000
χ3422-22-200-2222220002-22-200-2-2002-22-200002-20000-2-222000000000000000000
χ3522-22-200-2−1−i3−1+i32−1−i3−1+i30002-22-2001+i31−i300−1−i31+i3−1+i31−i300002-200001+i31−i3−1−i3−1+i3000000000000000000
χ3622-22-200-2−1+i3−1−i32−1+i3−1−i30002-22-2001−i31+i300−1+i31−i3−1−i31+i300002-200001−i31+i3−1+i3−1−i3000000000000000000
χ3722-2-2222022022-200-222-200-2-200-22-222222002-2000000-200-200000000000000
χ3822-2-22220−1−i3−1+i30−1−i3−1+i3-200-222-2001+i31−i3001+i3−1−i31−i3−1+i3−1−i3−1−i3−1+i3−1+i3002-20000001+i3001−i300000000000000
χ3922-2-22220−1+i3−1−i30−1+i3−1−i3-200-222-2001−i31+i3001−i3−1+i31+i3−1−i3−1+i3−1+i3−1−i3−1−i3002-20000001−i3001+i300000000000000
χ4022-2-22-2-2022022200-222-200-2-200-22-22-2-2-2-200-22000000200200000000000000
χ4122-2-22-2-20−1−i3−1+i30−1−i3−1+i3200-222-2001+i31−i3001+i3−1−i31−i3−1+i31+i31+i31−i31−i300-22000000−1−i300−1+i300000000000000
χ4222-2-22-2-20−1+i3−1−i30−1+i3−1−i3200-222-2001−i31+i3001−i3−1+i31+i3−1−i31−i31−i31+i31+i300-22000000−1+i300−1−i300000000000000
χ433333333300300333-1-1-1-133003300000000-1-1-1-1-1-10000000000-1-1-1-100000000
χ443333333300300333-1-1-1-1-3-300-3-300000000-1-1-1-1-1-10000000000111100000000
χ453333333-300-3003-3-3-1-1-1-13300-3-30000000011-1-1110000000000-1-11100000000
χ463333333-300-3003-3-3-1-1-1-1-3-300330000000011-1-111000000000011-1-100000000
χ4733333-3-3300300-3-3-3-1-1-1-13-3003-300000000-1-111110000000000-11-1100000000
χ4833333-3-3300300-3-3-3-1-1-1-1-3300-3300000000-1-1111100000000001-11-100000000
χ4933333-3-3-300-300-333-1-1-1-13-300-33000000001111-1-10000000000-111-100000000
χ5033333-3-3-300-300-333-1-1-1-1-33003-3000000001111-1-100000000001-1-1100000000
χ51666-6-60000000006i−6i22-2-2000000000000000000−2i2i0000000000000000000000
χ52666-6-6000000000−6i6i22-2-20000000000000000002i−2i0000000000000000000000
χ5366-66-600600-600000-22-22000000000000002-200000000000000000000000000
χ5466-66-600-600600000-22-2200000000000000-2200000000000000000000000000
χ5566-6-6666000000-6002-2-220000000000000000-22000000000000000000000000
χ5666-6-66-6-60000006002-2-2200000000000000002-2000000000000000000000000
χ578-800042−420-4-40440000000000000000022−2222−220000000000000000000000000000
χ588-800042−4202+2i32−2i30−2−2i3−2+2i300000000000000000−2ζ7+2ζ132ζ7−2ζ132ζ5−2ζ23−2ζ5+2ζ230000000000000000000000000000
χ598-800042−4202−2i32+2i30−2+2i3−2−2i3000000000000000002ζ5−2ζ23−2ζ5+2ζ23−2ζ7+2ζ132ζ7−2ζ130000000000000000000000000000
χ608-8000−42420-4-404400000000000000000−2222−22220000000000000000000000000000
χ618-8000−424202+2i32−2i30−2−2i3−2+2i3000000000000000002ζ7−2ζ13−2ζ7+2ζ13−2ζ5+2ζ232ζ5−2ζ230000000000000000000000000000
χ628-8000−424202−2i32+2i30−2+2i3−2−2i300000000000000000−2ζ5+2ζ232ζ5−2ζ232ζ7−2ζ13−2ζ7+2ζ130000000000000000000000000000

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