Finite Group Databasebeta

← Group #72258852

Character table — Group #72258852

Order 1536.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76
size111122333344666666666688881212121212121212121212121212161616161616161616162424242432323232323232323232323248486464646464646464
order1222442222244444444444444424444444444444334466666644441212121212121212121212124466121212121212
χ11111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111−1−i32−1+i3211−1−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+i32−1+i32−1+i3211−1−i32−1+i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32
χ31111111111111111111111111111111111111111−1+i32−1−i3211−1+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−i32−1−i32−1−i3211−1+i32−1−i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32
χ41111111111111111111111-1-1-1-11111111111111111-1-1111111-1-1-1-111-1-1-1-111-1-1-1-1-1-1111-1-11-1-1
χ51111111111111111111111-1-1-1-111111111111111−1−i32−1+i32-1-1−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32-1-1-1-1−1−i32−1−i321+i321+i321+i321+i32−1+i32−1+i321−i321−i321−i321−i32-1-1−1−i32−1+i32−1−i321+i321+i32−1+i321−i321−i32
χ61111111111111111111111-1-1-1-111111111111111−1+i32−1−i32-1-1−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32-1-1-1-1−1+i32−1+i321−i321−i321−i321−i32−1−i32−1−i321+i321+i321+i321+i32-1-1−1+i32−1−i32−1+i321−i321−i32−1−i321+i321+i32
χ71111111111-1-111111111111111-1-11111-1-1-1-1-1-1-1-111-1-11111111111111111111111-1-1-1-1-1-1-1-1-1-1
χ81111111111-1-111111111111111-1-11111-1-1-1-1-1-1-1-1−1−i32−1+i32-1-1−1−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+i32−1+i32−1+i32-1-11+i321−i321+i321+i321+i321−i321−i321−i32
χ91111111111-1-111111111111111-1-11111-1-1-1-1-1-1-1-1−1+i32−1−i32-1-1−1+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−i32−1−i32−1−i32-1-11−i321+i321−i321−i321−i321+i321+i321+i32
χ101111111111-1-11111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111111111-1-1-1-111-1-1-1-111-1-1-1-111-1-1-111-111
χ111111111111-1-11111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1−1−i32−1+i3211−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32-1-1-1-1−1−i32−1−i321+i321+i321+i321+i32−1+i32−1+i321−i321−i321−i321−i32111+i321−i321+i32−1−i32−1−i321−i32−1+i32−1+i32
χ121111111111-1-11111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1−1+i32−1−i3211−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32-1-1-1-1−1+i32−1+i321−i321−i321−i321−i32−1−i32−1−i321+i321+i321+i321+i32111−i321+i321−i32−1+i32−1+i321+i32−1−i32−1−i32
χ131111-1-111111-1-1-11111111111-1-11-1-1-1-1-11111-1-1-1-1111-111111111-1-1-1-111-1-1-1-111-1-11-111-11-1-11-1
χ141111-1-111111-1-1-11111111111-1-11-1-1-1-1-11111-1-1-1-1−1−i32−1+i321-1−1−i32−1−i32−1−i32−1+i32−1+i32−1+i3211-1-11+i321+i32−1−i32−1−i321+i321+i321−i321−i32−1+i32−1+i321−i321−i321-1−1−i32−1+i321+i32−1−i321+i321−i32−1+i321−i32
χ151111-1-111111-1-1-11111111111-1-11-1-1-1-1-11111-1-1-1-1−1+i32−1−i321-1−1+i32−1+i32−1+i32−1−i32−1−i32−1−i3211-1-11−i321−i32−1+i32−1+i321−i321−i321+i321+i32−1−i32−1−i321+i321+i321-1−1+i32−1−i321−i32−1+i321−i321+i32−1−i321+i32
χ161111-1-111111-1-1-111111111-1-1111-1-1-1-1-11111-1-1-1-111-11111111-1-111-1-1-1-111-1-1-1-111-1111-1-11-1-11
χ171111-1-111111-1-1-111111111-1-1111-1-1-1-1-11111-1-1-1-1−1−i32−1+i32-11−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32-1-1111+i321+i321+i321+i32−1−i32−1−i321−i321−i321−i321−i32−1+i32−1+i32-11−1−i32−1+i321+i321+i32−1−i321−i321−i32−1+i32
χ181111-1-111111-1-1-111111111-1-1111-1-1-1-1-11111-1-1-1-1−1+i32−1−i32-11−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32-1-1111−i321−i321−i321−i32−1+i32−1+i321+i321+i321+i321+i32−1−i32−1−i32-11−1+i32−1−i321−i321−i32−1+i321+i321+i32−1−i32
χ191111-1-11111-11-1-11111111111-1-1-11-1-1-1-1-1-1-1-1111111-1111111111-1-1-1-111-1-1-1-111-1-1-11-1-11-111-11
χ201111-1-11111-11-1-11111111111-1-1-11-1-1-1-1-1-1-1-11111−1−i32−1+i32-11−1−i32−1−i32−1−i32−1+i32−1+i32−1+i3211-1-11+i321+i32−1−i32−1−i321+i321+i321−i321−i32−1+i32−1+i321−i321−i32-111+i321−i32−1−i321+i32−1−i32−1+i321−i32−1+i32
χ211111-1-11111-11-1-11111111111-1-1-11-1-1-1-1-1-1-1-11111−1+i32−1−i32-11−1+i32−1+i32−1+i32−1−i32−1−i32−1−i3211-1-11−i321−i32−1+i32−1+i321−i321−i321+i321+i32−1−i32−1−i321+i321+i32-111−i321+i32−1+i321−i32−1+i32−1−i321+i32−1−i32
χ221111-1-11111-11-1-111111111-1-111-11-1-1-1-1-1-1-1-11111111-1111111-1-111-1-1-1-111-1-1-1-1111-1-1-111-111-1
χ231111-1-11111-11-1-111111111-1-111-11-1-1-1-1-1-1-1-11111−1−i32−1+i321-1−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32-1-1111+i321+i321+i321+i32−1−i32−1−i321−i321−i321−i321−i32−1+i32−1+i321-11+i321−i32−1−i32−1−i321+i32−1+i32−1+i321−i32
χ241111-1-11111-11-1-111111111-1-111-11-1-1-1-1-1-1-1-11111−1+i32−1−i321-1−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32-1-1111−i321−i321−i321−i32−1+i32−1+i321+i321+i321+i321+i32−1−i32−1−i321-11−i321+i32−1+i32−1+i321−i32−1−i32−1−i321+i32
χ2522-2-20022-2-200002222-2-2-2-2002i−2i0000000000000022002-2-22-2-2002i−2i00002i−2i00002i−2i0000000000
χ2622-2-20022-2-200002222-2-2-2-2002i−2i00000000000000−1−i3−1+i300−1−i31+i31+i3−1+i31−i31−i3002i−2i00002ζ11−2ζ1100002ζ7−2ζ70000000000
χ2722-2-20022-2-200002222-2-2-2-2002i−2i00000000000000−1+i3−1−i300−1+i31−i31−i3−1−i31+i31+i3002i−2i00002ζ7−2ζ700002ζ11−2ζ110000000000
χ2822-2-20022-2-200002222-2-2-2-200−2i2i0000000000000022002-2-22-2-200−2i2i0000−2i2i0000−2i2i0000000000
χ2922-2-20022-2-200002222-2-2-2-200−2i2i00000000000000−1−i3−1+i300−1−i31+i31+i3−1+i31−i31−i300−2i2i0000−2ζ112ζ110000−2ζ72ζ70000000000
χ3022-2-20022-2-200002222-2-2-2-200−2i2i00000000000000−1+i3−1−i300−1+i31−i31−i3−1−i31+i31+i300−2i2i0000−2ζ72ζ70000−2ζ112ζ110000000000
χ312-22-2002-22-2000022-2-222-2-22i−2i00000000000000002200-22-2-22-22i−2i00002i−2i00002i−2i000000000000
χ322-22-2002-22-2000022-2-222-2-22i−2i0000000000000000−1−i3−1+i3001+i3−1−i31+i31−i3−1+i31−i32i−2i00002ζ11−2ζ1100002ζ7−2ζ7000000000000
χ332-22-2002-22-2000022-2-222-2-22i−2i0000000000000000−1+i3−1−i3001−i3−1+i31−i31+i3−1−i31+i32i−2i00002ζ7−2ζ700002ζ11−2ζ11000000000000
χ342-22-2002-22-2000022-2-222-2-2−2i2i00000000000000002200-22-2-22-2−2i2i0000−2i2i0000−2i2i000000000000
χ352-22-2002-22-2000022-2-222-2-2−2i2i0000000000000000−1−i3−1+i3001+i3−1−i31+i31−i3−1+i31−i3−2i2i0000−2ζ112ζ110000−2ζ72ζ7000000000000
χ362-22-2002-22-2000022-2-222-2-2−2i2i0000000000000000−1+i3−1−i3001−i3−1+i31−i31+i3−1−i31+i3−2i2i0000−2ζ72ζ70000−2ζ112ζ11000000000000
χ372-2-222i−2i2-2-22002i−2i22-2-2-2-2220000002i2i−2i−2i000000002200-2-22-2-2200002i−2i00002i−2i00000000000000
χ382-2-222i−2i2-2-22002i−2i22-2-2-2-2220000002i2i−2i−2i00000000−1−i3−1+i3001+i31+i3−1−i31−i31−i3−1+i300002ζ11−2ζ1100002ζ7−2ζ700000000000000
χ392-2-222i−2i2-2-22002i−2i22-2-2-2-2220000002i2i−2i−2i00000000−1+i3−1−i3001−i31−i3−1+i31+i31+i3−1−i300002ζ7−2ζ700002ζ11−2ζ1100000000000000
χ402-2-22−2i2i2-2-2200−2i2i22-2-2-2-222000000−2i−2i2i2i000000002200-2-22-2-220000−2i2i0000−2i2i00000000000000
χ412-2-22−2i2i2-2-2200−2i2i22-2-2-2-222000000−2i−2i2i2i00000000−1−i3−1+i3001+i31+i3−1−i31−i31−i3−1+i30000−2ζ112ζ110000−2ζ72ζ700000000000000
χ422-2-22−2i2i2-2-2200−2i2i22-2-2-2-222000000−2i−2i2i2i00000000−1+i3−1−i3001−i31−i3−1+i31+i31+i3−1−i30000−2ζ72ζ70000−2ζ112ζ1100000000000000
χ4333333333333333-1-1-1-1-1-1-1-1333333-1-1-1-1-1-1-1-1-1-1-1-10033000000-1-1-1-1000000000000-1-100000000
χ4433333333333333-1-1-1-1-1-1-1-1-3-3-3-333-1-1-1-1-1-1-1-1-1-1-1-100-3-300000011110000000000001100000000
χ453333333333-3-333-1-1-1-1-1-1-1-13333-3-3-1-1-1-11111111100-3-3000000-1-1-1-10000000000001100000000
χ463333333333-3-333-1-1-1-1-1-1-1-1-3-3-3-3-3-3-1-1-1-11111111100330000001111000000000000-1-100000000
χ473333-3-333333-3-3-3-1-1-1-1-1-1-1-133-3-33-31111-1-1-1-11111003-3000000-1-111000000000000-1100000000
χ483333-3-333333-3-3-3-1-1-1-1-1-1-1-1-3-3333-31111-1-1-1-1111100-3300000011-1-10000000000001-100000000
χ493333-3-33333-33-3-3-1-1-1-1-1-1-1-133-3-3-3311111111-1-1-1-100-33000000-1-1110000000000001-100000000
χ503333-3-33333-33-3-3-1-1-1-1-1-1-1-1-3-333-3311111111-1-1-1-1003-300000011-1-1000000000000-1100000000
χ51666666-2-2-2-266-2-22i−2i2i−2i2i−2i2i−2i0000-2-22i−2i2i−2i2i2i−2i−2i2i2i−2i−2i000000000000000000000000000000000000
χ52666666-2-2-2-266-2-2−2i2i−2i2i−2i2i−2i2i0000-2-2−2i2i−2i2i−2i−2i2i2i−2i−2i2i2i000000000000000000000000000000000000
χ53666666-2-2-2-2-6-6-2-22i−2i2i−2i2i−2i2i−2i0000222i−2i2i−2i−2i−2i2i2i−2i−2i2i2i000000000000000000000000000000000000
χ54666666-2-2-2-2-6-6-2-2−2i2i−2i2i−2i2i−2i2i000022−2i2i−2i2i2i2i−2i−2i2i2i−2i−2i000000000000000000000000000000000000
χ556666-6-6-2-2-2-26-6222i−2i2i−2i2i−2i2i−2i0000-22−2i2i−2i2i2i2i−2i−2i−2i−2i2i2i000000000000000000000000000000000000
χ566666-6-6-2-2-2-26-622−2i2i−2i2i−2i2i−2i2i0000-222i−2i2i−2i−2i−2i2i2i2i2i−2i−2i000000000000000000000000000000000000
χ576666-6-6-2-2-2-2-66222i−2i2i−2i2i−2i2i−2i00002-2−2i2i−2i2i−2i−2i2i2i2i2i−2i−2i000000000000000000000000000000000000
χ586666-6-6-2-2-2-2-6622−2i2i−2i2i−2i2i−2i2i00002-22i−2i2i−2i2i2i−2i−2i−2i−2i2i2i000000000000000000000000000000000000
χ5966-6-60066-6-60000-2-2-2-22222006i−6i00000000000000000000000000−2i2i0000000000000000000000
χ6066-6-60066-6-60000-2-2-2-2222200−6i6i000000000000000000000000002i−2i0000000000000000000000
χ616-66-6006-66-60000-2-222-2-2226i−6i00000000000000000000000000−2i2i000000000000000000000000
χ626-66-6006-66-60000-2-222-2-222−6i6i000000000000000000000000002i−2i000000000000000000000000
χ636-6-666i−6i6-6-66006i−6i-2-22222-2-2000000−2i−2i2i2i00000000000000000000000000000000000000000000
χ646-6-666i−6i-222-200−2i2i2i−2i−2i2i−2i2i2i−2i000000-222-22−2i−2+2i2+2i−2−2i2+2i−2−2i2−2i−2+2i000000000000000000000000000000000000
χ656-6-666i−6i-222-200−2i2i2i−2i−2i2i−2i2i2i−2i000000-222-2−2+2i2−2i−2−2i2+2i−2−2i2+2i−2+2i2−2i000000000000000000000000000000000000
χ666-6-666i−6i-222-200−2i2i−2i2i2i−2i2i−2i−2i2i0000002-2-222+2i−2−2i2−2i−2+2i−2+2i2−2i−2−2i2+2i000000000000000000000000000000000000
χ676-6-666i−6i-222-200−2i2i−2i2i2i−2i2i−2i−2i2i0000002-2-22−2−2i2+2i−2+2i2−2i2−2i−2+2i2+2i−2−2i000000000000000000000000000000000000
χ686-6-66−6i6i6-6-6600−6i6i-2-22222-2-20000002i2i−2i−2i00000000000000000000000000000000000000000000
χ696-6-66−6i6i-222-2002i−2i2i−2i−2i2i−2i2i2i−2i0000002-2-222−2i−2+2i2+2i−2−2i−2−2i2+2i−2+2i2−2i000000000000000000000000000000000000
χ706-6-66−6i6i-222-2002i−2i2i−2i−2i2i−2i2i2i−2i0000002-2-22−2+2i2−2i−2−2i2+2i2+2i−2−2i2−2i−2+2i000000000000000000000000000000000000
χ716-6-66−6i6i-222-2002i−2i−2i2i2i−2i2i−2i−2i2i000000-222-22+2i−2−2i2−2i−2+2i2−2i−2+2i2+2i−2−2i000000000000000000000000000000000000
χ726-6-66−6i6i-222-2002i−2i−2i2i2i−2i2i−2i−2i2i000000-222-2−2−2i2+2i−2+2i2−2i−2+2i2−2i−2−2i2+2i000000000000000000000000000000000000
χ731212-12-1200-4-44400004i−4i4i−4i−4i4i−4i4i000000000000000000000000000000000000000000000000000000
χ741212-12-1200-4-4440000−4i4i−4i4i4i−4i4i−4i000000000000000000000000000000000000000000000000000000
χ7512-1212-1200-44-4400004i−4i−4i4i4i−4i−4i4i000000000000000000000000000000000000000000000000000000
χ7612-1212-1200-44-440000−4i4i4i−4i−4i4i4i−4i000000000000000000000000000000000000000000000000000000

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