Finite Group Databasebeta

← Group #72258924

Character table — Group #72258924

Order 1536.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64
size11113333488888812121212121212121216161616161616161616162424242424243232323232323232323232324848486464646464646464
order1222222222222222444444443344466666622444466666666666644466121212121212
χ11111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111−1−i32−1+i32111−1−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+i32−1+i32111−1−i32−1+i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32
χ3111111111111111111111111−1+i32−1−i32111−1+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−i32−1−i32111−1+i32−1−i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32
χ411111111111-1-1-1-1111111111111-1-1111111-1-111-1-111-1-1-1-111-1-1-1-1-11-1111-1-11-1-1
χ511111111111-1-1-1-1111111111−1−i32−1+i321-1-1−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32-1-111-1-1−1−i32−1−i321+i321+i321+i321+i32−1+i32−1+i321−i321−i321−i321−i32-11-1−1−i32−1+i32−1−i321+i321+i32−1+i321−i321−i32
χ611111111111-1-1-1-1111111111−1+i32−1−i321-1-1−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32-1-111-1-1−1+i32−1+i321−i321−i321−i321−i32−1−i32−1−i321+i321+i321+i321+i32-11-1−1+i32−1−i32−1+i321−i321−i32−1−i321+i321+i32
χ7111111111-1-111-1-111111111111-11-1111111-1-1-1-111-1-111-1-1-1-111-1-1-1-1111-11-1-11-1
χ8111111111-1-111-1-1111111111−1−i32−1+i32-11-1−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32-1-1-1-1111+i321+i32−1−i32−1−i321+i321+i321−i321−i32−1+i32−1+i321−i321−i32-1-11−1−i32−1+i321+i32−1−i321+i321−i32−1+i321−i32
χ9111111111-1-111-1-1111111111−1+i32−1−i32-11-1−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32-1-1-1-1111−i321−i32−1+i32−1+i321−i321−i321+i321+i32−1−i32−1−i321+i321+i32-1-11−1+i32−1−i321−i32−1+i321−i321+i32−1−i321+i32
χ10111111111-1-1-1-11111111111111-1-1111111111-1-1-1-1-1-1-1-111-1-1-1-1111-1-111-1-11-1-11
χ11111111111-1-1-1-111111111111−1−i32−1+i32-1-11−1−i32−1−i32−1−i32−1+i32−1+i32−1+i3211-1-1-1-11+i321+i321+i321+i32−1−i32−1−i321−i321−i321−i321−i32−1+i32−1+i321-1-1−1−i32−1+i321+i321+i32−1−i321−i321−i32−1+i32
χ12111111111-1-1-1-111111111111−1+i32−1−i32-1-11−1+i32−1+i32−1+i32−1−i32−1−i32−1−i3211-1-1-1-11−i321−i321−i321−i32−1+i32−1+i321+i321+i321+i321+i32−1−i32−1−i321-1-1−1+i32−1−i321−i321−i32−1+i321+i321+i32−1−i32
χ1311111111-1111111-11111-1-1-1-111-1-1-1111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1
χ1411111111-1111111-11111-1-1-1-1−1−i32−1+i32-1-1-1−1−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+i32−1+i32-1-1-11+i321−i321+i321+i321+i321−i321−i321−i32
χ1511111111-1111111-11111-1-1-1-1−1+i32−1−i32-1-1-1−1+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−i32−1−i32-1-1-11−i321+i321−i321−i321−i321+i321+i321+i32
χ1611111111-111-1-1-1-1-11111-1-1-1-111-111111111-1-111-1-111-1-1-1-111-1-1-1-11-11-1-1-111-111
χ1711111111-111-1-1-1-1-11111-1-1-1-1−1−i32−1+i32-111−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32-1-111-1-1−1−i32−1−i321+i321+i321+i321+i32−1+i32−1+i321−i321−i321−i321−i321-111+i321−i321+i32−1−i32−1−i321−i32−1+i32−1+i32
χ1811111111-111-1-1-1-1-11111-1-1-1-1−1+i32−1−i32-111−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32-1-111-1-1−1+i32−1+i321−i321−i321−i321−i32−1−i32−1−i321+i321+i321+i321+i321-111−i321+i321−i32−1+i32−1+i321+i32−1−i32−1−i32
χ1911111111-1-1-111-1-1-11111-1-1-1-1111-11111111-1-1-1-111-1-111-1-1-1-111-1-111-1-1-11-111-11
χ2011111111-1-1-111-1-1-11111-1-1-1-1−1−i32−1+i321-11−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32-1-1-1-1111+i321+i32−1−i32−1−i321+i321+i321−i321−i32−1+i32−1+i321−i321−i3211-11+i321−i32−1−i321+i32−1−i32−1+i321−i32−1+i32
χ2111111111-1-1-111-1-1-11111-1-1-1-1−1+i32−1−i321-11−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32-1-1-1-1111−i321−i32−1+i32−1+i321−i321−i321+i321+i32−1−i32−1−i321+i321+i3211-11−i321+i32−1+i321−i32−1+i32−1−i321+i32−1−i32
χ2211111111-1-1-1-1-111-11111-1-1-1-11111-111111111-1-1-1-1-1-1-1-111-1-1-1-111-111-1-111-111-1
χ2311111111-1-1-1-1-111-11111-1-1-1-1−1−i32−1+i3211-1−1−i32−1−i32−1−i32−1+i32−1+i32−1+i3211-1-1-1-11+i321+i321+i321+i32−1−i32−1−i321−i321−i321−i321−i32−1+i32−1+i32-1111+i321−i32−1−i32−1−i321+i32−1+i32−1+i321−i32
χ2411111111-1-1-1-1-111-11111-1-1-1-1−1+i32−1−i3211-1−1+i32−1+i32−1+i32−1−i32−1−i32−1−i3211-1-1-1-11−i321−i321−i321−i32−1+i32−1+i321+i321+i321+i321+i32−1−i32−1−i32-1111−i321+i32−1+i32−1+i321−i32−1−i32−1−i321+i32
χ2522-2-2-22-220002-200022-2-20000220002-2-22-2-200002-2002-200002-20000000000000
χ2622-2-2-22-220002-200022-2-20000−1−i3−1+i3000−1−i31+i31+i3−1+i31−i31−i300002-200−1−i31+i30000−1+i31−i30000000000000
χ2722-2-2-22-220002-200022-2-20000−1+i3−1−i3000−1+i31−i31−i3−1−i31+i31+i300002-200−1+i31−i30000−1−i31+i30000000000000
χ2822-2-2-22-22000-2200022-2-20000220002-2-22-2-20000-2200-220000-220000000000000
χ2922-2-2-22-22000-2200022-2-20000−1−i3−1+i3000−1−i31+i31+i3−1+i31−i31−i30000-22001+i3−1−i300001−i3−1+i30000000000000
χ3022-2-2-22-22000-2200022-2-20000−1+i3−1−i3000−1+i31−i31−i3−1−i31+i31+i30000-22001−i3−1+i300001+i3−1−i30000000000000
χ312-22-2-2-22202-2000002-22-2000022000-22-2-22-2002-2002-200002-2000000000000000
χ322-22-2-2-22202-2000002-22-20000−1−i3−1+i30001+i3−1−i31+i31−i3−1+i31−i3002-200−1−i31+i30000−1+i31−i3000000000000000
χ332-22-2-2-22202-2000002-22-20000−1+i3−1−i30001−i3−1+i31−i31+i3−1−i31+i3002-200−1+i31−i30000−1−i31+i3000000000000000
χ342-22-2-2-2220-22000002-22-2000022000-22-2-22-200-2200-220000-22000000000000000
χ352-22-2-2-2220-22000002-22-20000−1−i3−1+i30001+i3−1−i31+i31−i3−1+i31−i300-22001+i3−1−i300001−i3−1+i3000000000000000
χ362-22-2-2-2220-22000002-22-20000−1+i3−1−i30001−i3−1+i31−i31+i3−1−i31+i300-22001−i3−1+i300001+i3−1−i3000000000000000
χ372-2-222-2-22000002-202-2-22000022000-2-22-2-222-2000000002-200002-200000000000
χ382-2-222-2-22000002-202-2-220000−1−i3−1+i30001+i31+i3−1−i31−i31−i3−1+i32-200000000−1−i31+i30000−1+i31−i300000000000
χ392-2-222-2-22000002-202-2-220000−1+i3−1−i30001−i31−i3−1+i31+i31+i3−1−i32-200000000−1+i31−i30000−1−i31+i300000000000
χ402-2-222-2-2200000-2202-2-22000022000-2-22-2-22-2200000000-220000-2200000000000
χ412-2-222-2-2200000-2202-2-220000−1−i3−1+i30001+i31+i3−1−i31−i31−i3−1+i3-22000000001+i3−1−i300001−i3−1+i300000000000
χ422-2-222-2-2200000-2202-2-220000−1+i3−1−i30001−i31−i3−1+i31+i31+i3−1−i3-22000000001−i3−1+i300001+i3−1−i300000000000
χ433333333333333333-1-1-1-1-1-1-1-100333000000-1-1-1-1-1-1000000000000-1-1-100000000
χ4433333333333-3-3-3-33-1-1-1-1-1-1-1-1003-3-300000011-1-1110000000000001-1100000000
χ45333333333-3-333-3-33-1-1-1-1-1-1-1-100-33-30000001111-1-100000000000011-100000000
χ46333333333-3-3-3-3333-1-1-1-1-1-1-1-100-3-33000000-1-11111000000000000-11100000000
χ4733333333-3333333-3-1-1-1-1111100-3-3-3000000-1-1-1-1-1-100000000000011100000000
χ4833333333-333-3-3-3-3-3-1-1-1-1111100-33300000011-1-111000000000000-11-100000000
χ4933333333-3-3-333-3-3-3-1-1-1-11111003-330000001111-1-1000000000000-1-1100000000
χ5033333333-3-3-3-3-333-3-1-1-1-111110033-3000000-1-111110000000000001-1-100000000
χ5166-6-6-66-660006-6000-2-2220000000000000000000-2200000000000000000000000
χ5266-6-6-66-66000-66000-2-22200000000000000000002-200000000000000000000000
χ536-66-6-6-66606-600000-22-2200000000000000000-220000000000000000000000000
χ546-66-6-6-6660-6600000-22-22000000000000000002-20000000000000000000000000
χ556-6-666-6-66000006-60-222-2000000000000000-22000000000000000000000000000
χ566-6-666-6-6600000-660-222-20000000000000002-2000000000000000000000000000
χ5712121212-4-4-4-412000000-4000000000000000000000000000000000000000000000000
χ5812121212-4-4-4-4-120000004000000000000000000000000000000000000000000000000
χ591212-12-124-44-40000000000004i4i−4i−4i0000000000000000000000000000000000000000
χ601212-12-124-44-4000000000000−4i−4i4i4i0000000000000000000000000000000000000000
χ6112-1212-1244-4-40000000000004i−4i4i−4i0000000000000000000000000000000000000000
χ6212-1212-1244-4-4000000000000−4i4i−4i4i0000000000000000000000000000000000000000
χ6312-12-1212-444-40000000000004-4-440000000000000000000000000000000000000000
χ6412-12-1212-444-4000000000000-444-40000000000000000000000000000000000000000

Here i is the imaginary unit (i² = −1).