Finite Group Databasebeta

← Group #10593611

Character table — Group #10593611

Order 576.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69
size111122668888888812121212122424111122668888888812121212122424111122668888888812121212122424
order12224444366612121212288884436661212121236661212121262424242412123666121212123666121212126242424241212
χ1111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111-1-1-1-1-1-111111111111111111-1-1-1-1-1-111111111111111111-1-1-1-1-1-1
χ31111-1-1111111-1-1-1-1-111-1-11-11111-1-1111111-1-1-1-1-111-1-11-11111-1-1111111-1-1-1-1-111-1-11-1
χ41111-1-1111111-1-1-1-1-1-1-111-111111-1-1111111-1-1-1-1-1-1-111-111111-1-1111111-1-1-1-1-1-1-111-11
χ522222222-1-1-1-1-1-1-1-1200000022222222-1-1-1-1-1-1-1-1200000022222222-1-1-1-1-1-1-1-12000000
χ62222-2-222-1-1-1-11111-20000002222-2-222-1-1-1-11111-20000002222-2-222-1-1-1-11111-2000000
χ72-22-22i−2i00-11-11ii−i−i0−i2i22−2002-22-22i−2i00-11-11ii−i−i0−i2i22−2002-22-22i−2i00-11-11ii−i−i0−i2i22−200
χ82-22-22i−2i00-11-11ii−i−i0i2−i2−22002-22-22i−2i00-11-11ii−i−i0i2−i2−22002-22-22i−2i00-11-11ii−i−i0i2−i2−2200
χ92-22-2−2i2i00-11-11−i−iii0−i2i2−22002-22-2−2i2i00-11-11−i−iii0−i2i2−22002-22-2−2i2i00-11-11−i−iii0−i2i2−2200
χ102-22-2−2i2i00-11-11−i−iii0i2−i22−2002-22-2−2i2i00-11-11−i−iii0i2−i22−2002-22-2−2i2i00-11-11−i−iii0i2−i22−200
χ112-2-22002-22-2-22000000000002-2-22002-22-2-22000000000002-2-22002-22-2-2200000000000
χ122-2-22002-2-111-1−i3i3−i3i300000002-2-22002-2-111-1−i3i3−i3i300000002-2-22002-2-111-1−i3i3−i3i30000000
χ132-2-22002-2-111-1i3−i3i3−i300000002-2-22002-2-111-1i3−i3i3−i300000002-2-22002-2-111-1i3−i3i3−i30000000
χ14333333-1-100000000-11111-1-1333333-1-100000000-11111-1-1333333-1-100000000-11111-1-1
χ15333333-1-100000000-1-1-1-1-111333333-1-100000000-1-1-1-1-111333333-1-100000000-1-1-1-1-111
χ163333-3-3-1-100000000111-1-1-113333-3-3-1-100000000111-1-1-113333-3-3-1-100000000111-1-1-11
χ173333-3-3-1-1000000001-1-1111-13333-3-3-1-1000000001-1-1111-13333-3-3-1-1000000001-1-1111-1
χ1844-4-4000011-1-13−3−33000000044-4-4000011-1-13−3−33000000044-4-4000011-1-13−3−330000000
χ1944-4-4000011-1-1−333−3000000044-4-4000011-1-1−333−3000000044-4-4000011-1-1−333−30000000
χ2044-4-40000-2-2220000000000044-4-40000-2-2220000000000044-4-40000-2-22200000000000
χ214-44-44i−4i001-11-1−i−iii00000004-44-44i−4i001-11-1−i−iii00000004-44-44i−4i001-11-1−i−iii0000000
χ224-44-4−4i4i001-11-1ii−i−i00000004-44-4−4i4i001-11-1ii−i−i00000004-44-4−4i4i001-11-1ii−i−i0000000
χ236-6-6600-220000000000000006-6-6600-220000000000000006-6-6600-22000000000000000
χ2411111111111111111111111−1+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+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−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32
χ2511111111111111111-1-1-1-1-1-1−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−i321−i321−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+i321+i321+i321+i321+i321+i32
χ261111-1-1111111-1-1-1-1-111-1-11-1−1+i32−1+i32−1+i32−1+i321−i321−i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−i321−i32−1+i32−1+i321−i321−i32−1+i321−i32−1−i32−1−i32−1−i32−1−i321+i321+i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+i321+i32−1−i32−1−i321+i321+i32−1−i321+i32
χ271111-1-1111111-1-1-1-1-1-1-111-11−1+i32−1+i32−1+i32−1+i321−i321−i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−i321−i321−i321−i32−1+i32−1+i321−i32−1+i32−1−i32−1−i32−1−i32−1−i321+i321+i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+i321+i321+i321+i32−1−i32−1−i321+i32−1−i32
χ2822222222-1-1-1-1-1-1-1-12000000−1+i3−1+i3−1+i3−1+i3−1+i3−1+i3−1+i3−1+i31−i321−i321−i321−i321−i321−i321−i321−i32−1+i3000000−1−i3−1−i3−1−i3−1−i3−1−i3−1−i3−1−i3−1−i31+i321+i321+i321+i321+i321+i321+i321+i32−1−i3000000
χ292222-2-222-1-1-1-11111-2000000−1+i3−1+i3−1+i3−1+i31−i31−i3−1+i3−1+i31−i321−i321−i321−i32−1+i32−1+i32−1+i32−1+i321−i3000000−1−i3−1−i3−1−i3−1−i31+i31+i3−1−i3−1−i31+i321+i321+i321+i32−1−i32−1−i32−1−i32−1−i321+i3000000
χ302-22-22i−2i00-11-11ii−i−i0−i2i22−200−1+i31−i3−1+i31−i32ζ14−2ζ14001−i32−1+i321−i32−1+i32ζ14ζ14−ζ14−ζ140ζ5+ζ23−ζ5−ζ23ζ5−ζ23−ζ5+ζ2300−1−i31+i3−1−i31+i32ζ22−2ζ22001+i32−1−i321+i32−1−i32ζ22ζ22−ζ22−ζ220ζ7+ζ13−ζ7−ζ13−ζ7+ζ13ζ7−ζ1300
χ312-22-22i−2i00-11-11ii−i−i0i2−i2−2200−1+i31−i3−1+i31−i32ζ14−2ζ14001−i32−1+i321−i32−1+i32ζ14ζ14−ζ14−ζ140−ζ5−ζ23ζ5+ζ23−ζ5+ζ23ζ5−ζ2300−1−i31+i3−1−i31+i32ζ22−2ζ22001+i32−1−i321+i32−1−i32ζ22ζ22−ζ22−ζ220−ζ7−ζ13ζ7+ζ13ζ7−ζ13−ζ7+ζ1300
χ322-22-2−2i2i00-11-11−i−iii0−i2i2−2200−1+i31−i3−1+i31−i3−2ζ142ζ14001−i32−1+i321−i32−1+i32−ζ14−ζ14ζ14ζ140ζ5+ζ23−ζ5−ζ23−ζ5+ζ23ζ5−ζ2300−1−i31+i3−1−i31+i3−2ζ222ζ22001+i32−1−i321+i32−1−i32−ζ22−ζ22ζ22ζ220ζ7+ζ13−ζ7−ζ13ζ7−ζ13−ζ7+ζ1300
χ332-22-2−2i2i00-11-11−i−iii0i2−i22−200−1+i31−i3−1+i31−i3−2ζ142ζ14001−i32−1+i321−i32−1+i32−ζ14−ζ14ζ14ζ140−ζ5−ζ23ζ5+ζ23ζ5−ζ23−ζ5+ζ2300−1−i31+i3−1−i31+i3−2ζ222ζ22001+i32−1−i321+i32−1−i32−ζ22−ζ22ζ22ζ220−ζ7−ζ13ζ7+ζ13−ζ7+ζ13ζ7−ζ1300
χ342-2-22002-22-2-2200000000000−1+i31−i31−i3−1+i300−1+i31−i3−1+i31−i31−i3−1+i300000000000−1−i31+i31+i3−1−i300−1−i31+i3−1−i31+i31+i3−1−i300000000000
χ352-2-22002-2-111-1−i3i3−i3i30000000−1+i31−i31−i3−1+i300−1+i31−i31−i32−1+i32−1+i321−i323+i32−3−i323+i32−3−i320000000−1−i31+i31+i3−1−i300−1−i31+i31+i32−1−i32−1−i321+i32−3+i323−i32−3+i323−i320000000
χ362-2-22002-2-111-1i3−i3i3−i30000000−1+i31−i31−i3−1+i300−1+i31−i31−i32−1+i32−1+i321−i32−3−i323+i32−3−i323+i320000000−1−i31+i31+i3−1−i300−1−i31+i31+i32−1−i32−1−i321+i323−i32−3+i323−i32−3+i320000000
χ37333333-1-100000000-11111-1-1−3+3i32−3+3i32−3+3i32−3+3i32−3+3i32−3+3i321−i321−i32000000001−i32−1+i32−1+i32−1+i32−1+i321−i321−i32−3−3i32−3−3i32−3−3i32−3−3i32−3−3i32−3−3i321+i321+i32000000001+i32−1−i32−1−i32−1−i32−1−i321+i321+i32
χ38333333-1-100000000-1-1-1-1-111−3+3i32−3+3i32−3+3i32−3+3i32−3+3i32−3+3i321−i321−i32000000001−i321−i321−i321−i321−i32−1+i32−1+i32−3−3i32−3−3i32−3−3i32−3−3i32−3−3i32−3−3i321+i321+i32000000001+i321+i321+i321+i321+i32−1−i32−1−i32
χ393333-3-3-1-100000000111-1-1-11−3+3i32−3+3i32−3+3i32−3+3i323−3i323−3i321−i321−i3200000000−1+i32−1+i32−1+i321−i321−i321−i32−1+i32−3−3i32−3−3i32−3−3i32−3−3i323+3i323+3i321+i321+i3200000000−1−i32−1−i32−1−i321+i321+i321+i32−1−i32
χ403333-3-3-1-1000000001-1-1111-1−3+3i32−3+3i32−3+3i32−3+3i323−3i323−3i321−i321−i3200000000−1+i321−i321−i32−1+i32−1+i32−1+i321−i32−3−3i32−3−3i32−3−3i32−3−3i323+3i323+3i321+i321+i3200000000−1−i321+i321+i32−1−i32−1−i32−1−i321+i32
χ4144-4-4000011-1-13−3−330000000−2+2i3−2+2i32−2i32−2i30000−1+i32−1+i321−i321−i32−ζ14−2ζ22ζ14+2ζ22ζ14+2ζ22−ζ14−2ζ220000000−2−2i3−2−2i32+2i32+2i30000−1−i32−1−i321+i321+i322ζ14+ζ22−2ζ14−ζ22−2ζ14−ζ222ζ14+ζ220000000
χ4244-4-4000011-1-1−333−30000000−2+2i3−2+2i32−2i32−2i30000−1+i32−1+i321−i321−i32ζ14+2ζ22−ζ14−2ζ22−ζ14−2ζ22ζ14+2ζ220000000−2−2i3−2−2i32+2i32+2i30000−1−i32−1−i321+i321+i32−2ζ14−ζ222ζ14+ζ222ζ14+ζ22−2ζ14−ζ220000000
χ4344-4-40000-2-22200000000000−2+2i3−2+2i32−2i32−2i300001−i31−i3−1+i3−1+i300000000000−2−2i3−2−2i32+2i32+2i300001+i31+i3−1−i3−1−i300000000000
χ444-44-44i−4i001-11-1−i−iii0000000−2+2i32−2i3−2+2i32−2i34ζ14−4ζ1400−1+i321−i32−1+i321−i32−ζ14−ζ14ζ14ζ140000000−2−2i32+2i3−2−2i32+2i34ζ22−4ζ2200−1−i321+i32−1−i321+i32−ζ22−ζ22ζ22ζ220000000
χ454-44-4−4i4i001-11-1ii−i−i0000000−2+2i32−2i3−2+2i32−2i3−4ζ144ζ1400−1+i321−i32−1+i321−i32ζ14ζ14−ζ14−ζ140000000−2−2i32+2i3−2−2i32+2i3−4ζ224ζ2200−1−i321+i32−1−i321+i32ζ22ζ22−ζ22−ζ220000000
χ466-6-6600-22000000000000000−3+3i33−3i33−3i3−3+3i3001−i3−1+i3000000000000000−3−3i33+3i33+3i3−3−3i3001+i3−1−i3000000000000000
χ4711111111111111111111111−1−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−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+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32
χ4811111111111111111-1-1-1-1-1-1−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+i321+i321+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−i321−i321−i321−i321−i321−i32
χ491111-1-1111111-1-1-1-1-111-1-11-1−1−i32−1−i32−1−i32−1−i321+i321+i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+i321+i32−1−i32−1−i321+i321+i32−1−i321+i32−1+i32−1+i32−1+i32−1+i321−i321−i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−i321−i32−1+i32−1+i321−i321−i32−1+i321−i32
χ501111-1-1111111-1-1-1-1-1-1-111-11−1−i32−1−i32−1−i32−1−i321+i321+i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+i321+i321+i321+i32−1−i32−1−i321+i32−1−i32−1+i32−1+i32−1+i32−1+i321−i321−i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−i321−i321−i321−i32−1+i32−1+i321−i32−1+i32
χ5122222222-1-1-1-1-1-1-1-12000000−1−i3−1−i3−1−i3−1−i3−1−i3−1−i3−1−i3−1−i31+i321+i321+i321+i321+i321+i321+i321+i32−1−i3000000−1+i3−1+i3−1+i3−1+i3−1+i3−1+i3−1+i3−1+i31−i321−i321−i321−i321−i321−i321−i321−i32−1+i3000000
χ522222-2-222-1-1-1-11111-2000000−1−i3−1−i3−1−i3−1−i31+i31+i3−1−i3−1−i31+i321+i321+i321+i32−1−i32−1−i32−1−i32−1−i321+i3000000−1+i3−1+i3−1+i3−1+i31−i31−i3−1+i3−1+i31−i321−i321−i321−i32−1+i32−1+i32−1+i32−1+i321−i3000000
χ532-22-22i−2i00-11-11ii−i−i0−i2i22−200−1−i31+i3−1−i31+i32ζ22−2ζ22001+i32−1−i321+i32−1−i32ζ22ζ22−ζ22−ζ220ζ7+ζ13−ζ7−ζ13−ζ7+ζ13ζ7−ζ1300−1+i31−i3−1+i31−i32ζ14−2ζ14001−i32−1+i321−i32−1+i32ζ14ζ14−ζ14−ζ140ζ5+ζ23−ζ5−ζ23ζ5−ζ23−ζ5+ζ2300
χ542-22-22i−2i00-11-11ii−i−i0i2−i2−2200−1−i31+i3−1−i31+i32ζ22−2ζ22001+i32−1−i321+i32−1−i32ζ22ζ22−ζ22−ζ220−ζ7−ζ13ζ7+ζ13ζ7−ζ13−ζ7+ζ1300−1+i31−i3−1+i31−i32ζ14−2ζ14001−i32−1+i321−i32−1+i32ζ14ζ14−ζ14−ζ140−ζ5−ζ23ζ5+ζ23−ζ5+ζ23ζ5−ζ2300
χ552-22-2−2i2i00-11-11−i−iii0−i2i2−2200−1−i31+i3−1−i31+i3−2ζ222ζ22001+i32−1−i321+i32−1−i32−ζ22−ζ22ζ22ζ220ζ7+ζ13−ζ7−ζ13ζ7−ζ13−ζ7+ζ1300−1+i31−i3−1+i31−i3−2ζ142ζ14001−i32−1+i321−i32−1+i32−ζ14−ζ14ζ14ζ140ζ5+ζ23−ζ5−ζ23−ζ5+ζ23ζ5−ζ2300
χ562-22-2−2i2i00-11-11−i−iii0i2−i22−200−1−i31+i3−1−i31+i3−2ζ222ζ22001+i32−1−i321+i32−1−i32−ζ22−ζ22ζ22ζ220−ζ7−ζ13ζ7+ζ13−ζ7+ζ13ζ7−ζ1300−1+i31−i3−1+i31−i3−2ζ142ζ14001−i32−1+i321−i32−1+i32−ζ14−ζ14ζ14ζ140−ζ5−ζ23ζ5+ζ23ζ5−ζ23−ζ5+ζ2300
χ572-2-22002-22-2-2200000000000−1−i31+i31+i3−1−i300−1−i31+i3−1−i31+i31+i3−1−i300000000000−1+i31−i31−i3−1+i300−1+i31−i3−1+i31−i31−i3−1+i300000000000
χ582-2-22002-2-111-1−i3i3−i3i30000000−1−i31+i31+i3−1−i300−1−i31+i31+i32−1−i32−1−i321+i32−3+i323−i32−3+i323−i320000000−1+i31−i31−i3−1+i300−1+i31−i31−i32−1+i32−1+i321−i323+i32−3−i323+i32−3−i320000000
χ592-2-22002-2-111-1i3−i3i3−i30000000−1−i31+i31+i3−1−i300−1−i31+i31+i32−1−i32−1−i321+i323−i32−3+i323−i32−3+i320000000−1+i31−i31−i3−1+i300−1+i31−i31−i32−1+i32−1+i321−i32−3−i323+i32−3−i323+i320000000
χ60333333-1-100000000-11111-1-1−3−3i32−3−3i32−3−3i32−3−3i32−3−3i32−3−3i321+i321+i32000000001+i32−1−i32−1−i32−1−i32−1−i321+i321+i32−3+3i32−3+3i32−3+3i32−3+3i32−3+3i32−3+3i321−i321−i32000000001−i32−1+i32−1+i32−1+i32−1+i321−i321−i32
χ61333333-1-100000000-1-1-1-1-111−3−3i32−3−3i32−3−3i32−3−3i32−3−3i32−3−3i321+i321+i32000000001+i321+i321+i321+i321+i32−1−i32−1−i32−3+3i32−3+3i32−3+3i32−3+3i32−3+3i32−3+3i321−i321−i32000000001−i321−i321−i321−i321−i32−1+i32−1+i32
χ623333-3-3-1-100000000111-1-1-11−3−3i32−3−3i32−3−3i32−3−3i323+3i323+3i321+i321+i3200000000−1−i32−1−i32−1−i321+i321+i321+i32−1−i32−3+3i32−3+3i32−3+3i32−3+3i323−3i323−3i321−i321−i3200000000−1+i32−1+i32−1+i321−i321−i321−i32−1+i32
χ633333-3-3-1-1000000001-1-1111-1−3−3i32−3−3i32−3−3i32−3−3i323+3i323+3i321+i321+i3200000000−1−i321+i321+i32−1−i32−1−i32−1−i321+i32−3+3i32−3+3i32−3+3i32−3+3i323−3i323−3i321−i321−i3200000000−1+i321−i321−i32−1+i32−1+i32−1+i321−i32
χ6444-4-4000011-1-13−3−330000000−2−2i3−2−2i32+2i32+2i30000−1−i32−1−i321+i321+i322ζ14+ζ22−2ζ14−ζ22−2ζ14−ζ222ζ14+ζ220000000−2+2i3−2+2i32−2i32−2i30000−1+i32−1+i321−i321−i32−ζ14−2ζ22ζ14+2ζ22ζ14+2ζ22−ζ14−2ζ220000000
χ6544-4-4000011-1-1−333−30000000−2−2i3−2−2i32+2i32+2i30000−1−i32−1−i321+i321+i32−2ζ14−ζ222ζ14+ζ222ζ14+ζ22−2ζ14−ζ220000000−2+2i3−2+2i32−2i32−2i30000−1+i32−1+i321−i321−i32ζ14+2ζ22−ζ14−2ζ22−ζ14−2ζ22ζ14+2ζ220000000
χ6644-4-40000-2-22200000000000−2−2i3−2−2i32+2i32+2i300001+i31+i3−1−i3−1−i300000000000−2+2i3−2+2i32−2i32−2i300001−i31−i3−1+i3−1+i300000000000
χ674-44-44i−4i001-11-1−i−iii0000000−2−2i32+2i3−2−2i32+2i34ζ22−4ζ2200−1−i321+i32−1−i321+i32−ζ22−ζ22ζ22ζ220000000−2+2i32−2i3−2+2i32−2i34ζ14−4ζ1400−1+i321−i32−1+i321−i32−ζ14−ζ14ζ14ζ140000000
χ684-44-4−4i4i001-11-1ii−i−i0000000−2−2i32+2i3−2−2i32+2i3−4ζ224ζ2200−1−i321+i32−1−i321+i32ζ22ζ22−ζ22−ζ220000000−2+2i32−2i3−2+2i32−2i3−4ζ144ζ1400−1+i321−i32−1+i321−i32ζ14ζ14−ζ14−ζ140000000
χ696-6-6600-22000000000000000−3−3i33+3i33+3i3−3−3i3001+i3−1−i3000000000000000−3+3i33−3i33−3i3−3+3i3001−i3−1+i3000000000000000

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