Finite Group Databasebeta

← Group #72276435

Character table — Group #72276435

Order 2688.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76
size11244444667777888121212141416242424242424242428282828282828282828282828282828282828282828484848565656565656565656565656112112112112112112112112
order1222222471433662441414146641414141414282828224466666666666612121212121228282824666612121212121248121212122424
χ11111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111-1-1-1-11111-1-1-1-11111-1-1-1-111111-1-111-1-11111-1-1-1-111-1-1-1-1
χ311111111111111-1-1111111-1111-1-11-1-111111111111111111111111-1-111-1-111-1-11111-1-1-1-1-1-1-1-1
χ411111111111111-1-1111111-1111-1-11-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1111-1-1-1-1-1-1-1-1-1-111-1-111-1-11111
χ51111111111−1+i32−1−i32−1+i32−1−i32111111−1+i32−1−i321111111111111−1+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−i3211111−1+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
χ61111111111−1+i32−1−i32−1+i32−1−i32111111−1+i32−1−i32111111111-1-1-1-1−1+i32−1+i32−1−i32−1−i321−i321−i321+i321+i32−1+i32−1+i32−1−i32−1−i321−i321−i321+i321+i32−1+i32−1−i32111-1-1−1+i32−1−i321−i321+i32−1+i32−1−i32−1+i32−1−i321−i321+i32-1-1−1+i32−1−i321−i321+i321−i321+i32
χ71111111111−1+i32−1−i32−1+i32−1−i32-1-11111−1+i32−1−i32-1111-1-11-1-11111−1+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−i321-1-1111−i321+i32−1+i32−1−i321−i321+i32−1+i32−1−i32−1+i32−1−i32-1-11−i321+i321−i321+i321−i321+i32
χ81111111111−1+i32−1−i32−1+i32−1−i32-1-11111−1+i32−1−i32-1111-1-11-1-1-1-1-1-1−1+i32−1+i32−1−i32−1−i321−i321−i321+i321+i32−1+i32−1+i32−1−i32−1−i321−i321−i321+i321+i32−1+i32−1−i321-1-1-1-11−i321+i321−i321+i321−i321+i32−1+i32−1−i321−i321+i32111−i321+i32−1+i32−1−i32−1+i32−1−i32
χ91111111111−1−i32−1+i32−1−i32−1+i32111111−1−i32−1+i321111111111111−1−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+i3211111−1−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
χ101111111111−1−i32−1+i32−1−i32−1+i32111111−1−i32−1+i32111111111-1-1-1-1−1−i32−1−i32−1+i32−1+i321+i321+i321−i321−i32−1−i32−1−i32−1+i32−1+i321+i321+i321−i321−i32−1−i32−1+i32111-1-1−1−i32−1+i321+i321−i32−1−i32−1+i32−1−i32−1+i321+i321−i32-1-1−1−i32−1+i321+i321−i321+i321−i32
χ111111111111−1−i32−1+i32−1−i32−1+i32-1-11111−1−i32−1+i32-1111-1-11-1-11111−1−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+i321-1-1111+i321−i32−1−i32−1+i321+i321−i32−1−i32−1+i32−1−i32−1+i32-1-11+i321−i321+i321−i321+i321−i32
χ121111111111−1−i32−1+i32−1−i32−1+i32-1-11111−1−i32−1+i32-1111-1-11-1-1-1-1-1-1−1−i32−1−i32−1+i32−1+i321+i321+i321−i321−i32−1−i32−1−i32−1+i32−1+i321+i321+i321−i321−i32−1−i32−1+i321-1-1-1-11+i321−i321+i321−i321+i321−i32−1−i32−1+i321+i321−i32111+i321−i32−1−i32−1+i32−1−i32−1+i32
χ13111-1-111111111111-111111-11-1-11111111-1-1-1-1-1-111111111-1-1-1-111-1-1-1-1111-1-111-1-1111-1-1-111-1-1
χ14111-1-111111111111-111111-11-1-111111-1-111-1-1-1-1-1-1-1-11111111111-1-1-11-1111111-1-1-1-1-11-1-1-1-111
χ15111-1-1111111111-1-1-11111111-1-1-1-11-1-111-1-1-1-1-1-111111111-1-1-1-111-111-11-1-1-1-1-1-1-1-111-1111-1-111
χ16111-1-1111111111-1-1-11111111-1-1-1-11-1-1-1-111-1-1-1-1-1-1-1-11111111111-1111-1-1-111-1-1-1-1-1-11-11111-1-1
χ17111-1-111111−1+i32−1−i32−1+i32−1−i3211-1111−1+i32−1−i32-11-1-11111111-1-11−i321−i321+i321+i32−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1−i321−i321−i321+i321+i32−1+i32−1−i32-1-1-1-11−1+i32−1−i321−i321+i32−1+i32−1−i321−i321+i32−1+i32−1−i321-11−i321+i32−1+i32−1−i321−i321+i32
χ18111-1-111111−1+i32−1−i32−1+i32−1−i3211-1111−1+i32−1−i32-11-1-111111-1-1111−i321−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−i32-1-1-11-1−1+i32−1−i32−1+i32−1−i32−1+i32−1−i321−i321+i321−i321+i32-111−i321+i321−i321+i32−1+i32−1−i32
χ19111-1-111111−1+i32−1−i32−1+i32−1−i32-1-1-1111−1+i32−1−i3211-1-1-1-11-1-111-1-11−i321−i321+i321+i32−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1−i321−i321−i321+i321+i32−1+i32−1−i32-111-111−i321+i321−i321+i321−i321+i321−i321+i32−1+i32−1−i32-11−1+i32−1−i321−i321+i32−1+i32−1−i32
χ20111-1-111111−1+i32−1−i32−1+i32−1−i32-1-1-1111−1+i32−1−i3211-1-1-1-11-1-1-1-1111−i321−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−i32-1111-11−i321+i32−1+i32−1−i321−i321+i321−i321+i321−i321+i321-1−1+i32−1−i32−1+i32−1−i321−i321+i32
χ21111-1-111111−1−i32−1+i32−1−i32−1+i3211-1111−1−i32−1+i32-11-1-11111111-1-11+i321+i321−i321−i32−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1+i321+i321+i321−i321−i32−1−i32−1+i32-1-1-1-11−1−i32−1+i321+i321−i32−1−i32−1+i321+i321−i32−1−i32−1+i321-11+i321−i32−1−i32−1+i321+i321−i32
χ22111-1-111111−1−i32−1+i32−1−i32−1+i3211-1111−1−i32−1+i32-11-1-111111-1-1111+i321+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+i32-1-1-11-1−1−i32−1+i32−1−i32−1+i32−1−i32−1+i321+i321−i321+i321−i32-111+i321−i321+i321−i32−1−i32−1+i32
χ23111-1-111111−1−i32−1+i32−1−i32−1+i32-1-1-1111−1−i32−1+i3211-1-1-1-11-1-111-1-11+i321+i321−i321−i32−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1+i321+i321+i321−i321−i32−1−i32−1+i32-111-111+i321−i321+i321−i321+i321−i321+i321−i32−1−i32−1+i32-11−1−i32−1+i321+i321−i32−1−i32−1+i32
χ24111-1-111111−1−i32−1+i32−1−i32−1+i32-1-1-1111−1−i32−1+i3211-1-1-1-11-1-1-1-1111+i321+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+i32-1111-11+i321−i32−1−i32−1+i321+i321−i321+i321−i321+i321−i321-1−1−i32−1+i32−1−i32−1+i321+i321−i32
χ2522200-22-22222220002-2-222020000-2002200000022222-22-20000-2-20000-200000000-2-200000000
χ2622200-22-22222220002-2-222020000-200-2-2000000-2-2-2-22-22-20000-2-200002000000002200000000
χ2722200-22-222−1+i3−1−i3−1+i3−1−i30002-2-2−1+i3−1−i3020000-20022000000−1+i3−1+i3−1−i3−1−i3−1+i31−i3−1−i31+i300001−i31+i30000-2000000001−i31+i300000000
χ2822200-22-222−1+i3−1−i3−1+i3−1−i30002-2-2−1+i3−1−i3020000-200-2-20000001−i31−i31+i31+i3−1+i31−i3−1−i31+i300001−i31+i30000200000000−1+i3−1−i300000000
χ2922200-22-222−1−i3−1+i3−1−i3−1+i30002-2-2−1−i3−1+i3020000-20022000000−1−i3−1−i3−1+i3−1+i3−1−i31+i3−1+i31−i300001+i31−i30000-2000000001+i31−i300000000
χ3022200-22-222−1−i3−1+i3−1−i3−1+i30002-2-2−1−i3−1+i3020000-200-2-20000001+i31+i31−i31−i3−1−i31+i3−1+i31−i300001+i31−i30000200000000−1−i3−1+i300000000
χ3122200-2-222222220002-2-2220-20000200002200000000-2-2-2-2222222000-2000-2-200000000000000
χ3222200-2-222222220002-2-2220-2000020000-2-200000000-2-2-2-2-2-2-2-22200020002200000000000000
χ3322200-2-2222−1+i3−1−i3−1+i3−1−i30002-2-2−1+i3−1−i30-200002000022000000001−i31−i31+i31+i3−1+i3−1+i3−1−i3−1−i3−1+i3−1−i3000-20001−i31+i300000000000000
χ3422200-2-2222−1+i3−1−i3−1+i3−1−i30002-2-2−1+i3−1−i30-2000020000-2-2000000001−i31−i31+i31+i31−i31−i31+i31+i3−1+i3−1−i30002000−1+i3−1−i300000000000000
χ3522200-2-2222−1−i3−1+i3−1−i3−1+i30002-2-2−1−i3−1+i30-200002000022000000001+i31+i31−i31−i3−1−i3−1−i3−1+i3−1+i3−1−i3−1+i3000-20001+i31−i300000000000000
χ3622200-2-2222−1−i3−1+i3−1−i3−1+i30002-2-2−1−i3−1+i30-2000020000-2-2000000001+i31+i31−i31−i31+i31+i31−i31−i3−1−i3−1+i30002000−1−i3−1+i300000000000000
χ37222222-2-222222200-2222220-22200-200000022220000-22-220000-2-2-20000000000-2-20000000000
χ38222222-2-222−1+i3−1−i3−1+i3−1−i300-2222−1+i3−1−i30-22200-2000000−1+i3−1+i3−1−i3−1−i300001−i3−1+i31+i3−1−i300001−i31+i3-200000000001−i31+i30000000000
χ39222222-2-222−1−i3−1+i3−1−i3−1+i300-2222−1−i3−1+i30-22200-2000000−1−i3−1−i3−1+i3−1+i300001+i3−1−i31−i3−1+i300001+i31−i3-200000000001+i31−i30000000000
χ40222-2-22-2-2222222002222220-2-2-200-2000000-2-2-2-20000-22-220000-2-220000000000220000000000
χ41222-2-22-2-222−1+i3−1−i3−1+i3−1−i3002222−1+i3−1−i30-2-2-200-20000001−i31−i31+i31+i300001−i3−1+i31+i3−1−i300001−i31+i320000000000−1+i3−1−i30000000000
χ42222-2-22-2-222−1−i3−1+i3−1−i3−1+i3002222−1−i3−1+i30-2-2-200-20000001+i31+i31−i31−i300001+i3−1−i31−i3−1+i300001+i31−i320000000000−1−i3−1+i30000000000
χ4344-4000004444442-20-400-4-40000220-2-20000000000000000000000000002200-2-2000000000000
χ4444-400000444444-220-400-4-40000-2-2022000000000000000000000000000-2-20022000000000000
χ4544-40000044−2+2i3−2−2i3−2+2i3−2−2i32-20-4002−2i32+2i30000220-2-2000000000000000000000000000−1+i3−1−i3001−i31+i3000000000000
χ4644-40000044−2+2i3−2−2i3−2+2i3−2−2i3-220-4002−2i32+2i30000-2-20220000000000000000000000000001−i31+i300−1+i3−1−i3000000000000
χ4744-40000044−2−2i3−2+2i3−2−2i3−2+2i32-20-4002+2i32−2i30000220-2-2000000000000000000000000000−1−i3−1+i3001+i31−i3000000000000
χ4844-40000044−2−2i3−2+2i3−2−2i3−2+2i3-220-4002+2i32−2i30000-2-20220000000000000000000000000001+i31−i300−1−i3−1+i3000000000000
χ494-402-20004-444-4-400000000002-2000002-22-22-22-22-22-200002-22-20000000000000000000000000
χ504-402-20004-444-4-400000000002-200000-22-222-22-2-22-220000-22-220000000000000000000000000
χ514-402-20004-4−2+2i3−2−2i32−2i32+2i300000000002-2000002-22-2−1+i31−i3−1−i31+i3−1+i31−i3−1−i31+i30000−1+i31−i3−1−i31+i30000000000000000000000000
χ524-402-20004-4−2+2i3−2−2i32−2i32+2i300000000002-200000-22-22−1+i31−i3−1−i31+i31−i3−1+i31+i3−1−i300001−i3−1+i31+i3−1−i30000000000000000000000000
χ534-402-20004-4−2−2i3−2+2i32+2i32−2i300000000002-2000002-22-2−1−i31+i3−1+i31−i3−1−i31+i3−1+i31−i30000−1−i31+i3−1+i31−i30000000000000000000000000
χ544-402-20004-4−2−2i3−2+2i32+2i32−2i300000000002-200000-22-22−1−i31+i3−1+i31−i31+i3−1−i31−i3−1+i300001+i3−1−i31−i3−1+i30000000000000000000000000
χ554-40-220004-444-4-40000000000-22000002-2-22-22-222-22-20000-22-220000000000000000000000000
χ564-40-220004-444-4-40000000000-2200000-222-2-22-22-22-2200002-22-20000000000000000000000000
χ574-40-220004-4−2+2i3−2−2i32−2i32+2i30000000000-22000002-2-221−i3−1+i31+i3−1−i3−1+i31−i3−1−i31+i300001−i3−1+i31+i3−1−i30000000000000000000000000
χ584-40-220004-4−2+2i3−2−2i32−2i32+2i30000000000-2200000-222-21−i3−1+i31+i3−1−i31−i3−1+i31+i3−1−i30000−1+i31−i3−1−i31+i30000000000000000000000000
χ594-40-220004-4−2−2i3−2+2i32+2i32−2i30000000000-22000002-2-221+i3−1−i31−i3−1+i3−1−i31+i3−1+i31−i300001+i3−1−i31−i3−1+i30000000000000000000000000
χ604-40-220004-4−2−2i3−2+2i32+2i32−2i30000000000-2200000-222-21+i3−1−i31−i3−1+i31+i3−1−i31−i3−1+i30000−1−i31+i3−1+i31−i30000000000000000000000000
χ6166666666-1-10000666-1-1-1006-1-1-1-1-1-1-1-10000000000000000000000-1-1-100000000000000000000
χ6266666666-1-10000-6-66-1-1-100-6-1-1-111-1110000000000000000000000-11100000000000000000000
χ63666666-6-6-1-1000000-6-1-1-10001-1-1−i7i71−i7i700000000000000000000001−i7i700000000000000000000
χ64666666-6-6-1-1000000-6-1-1-10001-1-1i7−i71i7−i700000000000000000000001i7−i700000000000000000000
χ65666-6-6666-1-1000066-6-1-1-100-6-111-1-1-1-1-1000000000000000000000011100000000000000000000
χ66666-6-6666-1-10000-6-6-6-1-1-1006-11111-11100000000000000000000001-1-100000000000000000000
χ67666-6-66-6-6-1-10000006-1-1-1000111−i7i71−i7i70000000000000000000000-1i7−i700000000000000000000
χ68666-6-66-6-6-1-10000006-1-1-1000111i7−i71i7−i70000000000000000000000-1−i7i700000000000000000000
χ6912121200-1212-12-2-20000000-222000-20000200000000000000000000000000000000000000000000000
χ7012121200-12-1212-2-20000000-22200020000-200000000000000000000000000000000000000000000000
χ711212-1200000-2-200006-602−2i72i7000000−1−i7−1+i701+i71−i7000000000000000000000000000000000000000000000
χ721212-1200000-2-200006-6022i7−2i7000000−1+i7−1−i701−i71+i7000000000000000000000000000000000000000000000
χ731212-1200000-2-20000-6602−2i72i70000001+i71−i70−1−i7−1+i7000000000000000000000000000000000000000000000
χ741212-1200000-2-20000-66022i7−2i70000001−i71+i70−1+i7−1−i7000000000000000000000000000000000000000000000
χ7524-24012-12000-4400000000000000-2200000000000000000000000000000000000000000000000000
χ7624-240-1212000-44000000000000002-200000000000000000000000000000000000000000000000000

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