Finite Group Databasebeta

← Group #13167304

Character table — Group #13167304

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87
size111122222244444444444444444444448888888888888818182424242424242424242424242424242424243636363636363636363636363636363636108108108108
order1222223666333366666666666666666636666666666666444412121212121212121212121212121212444441212121212121212121212128888
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111111-1-1-1-1
χ4111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-11111-1-1-1-1-1-1-1-11111
χ51111-1-111111111-1-111111-1-1-1-111111111-1-1-1-1-1-1111-1-1-1-1111-1-1-111111111-1-1-1-1-1-1-111-1-111-1-11111-1-1-1-111-1-1
χ61111-1-111111111-1-111111-1-1-1-111111111-1-1-1-1-1-1111-1-1-1-1111-1-1-111111111-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111-1-111
χ71111-1-111111111-1-111111-1-1-1-111111111-1-1-1-1-1-1111-1-1-1-111-1111-1-1-1-1-1-1-1-1111111-111-1-111-1-11111-1-1-1-1-1-111
χ81111-1-111111111-1-111111-1-1-1-111111111-1-1-1-1-1-1111-1-1-1-111-1111-1-1-1-1-1-1-1-1111111-1-1-11111-1-1-1-1-1-1111111-1-1
χ92222222222222222222222222222222222222222222222-2-2000000000000000000-20000-2-2-2-2000000000000
χ10222222-1-1-1-122-1-1-1-1222-1-1222222-1-1-1-12-122-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-122-1-1-1-122-1-1-1-120000-1-1-1-1000000000000
χ11222222-1-1-1-122-1-1-1-1222-1-1222222-1-1-1-12-122-1-1-1-1-1-1-1-1-1-1-122-2-21111-2-21111-2-2111120000-1-1-1-1000000000000
χ12222222-1-1-1-122-1-1-1-1222-1-1222222-1-1-1-12-122-1-1-1-1-1-1-1-1-1-1-1-2-200−i3i3−i3i300−i3−i3i3i300−i3−i3i3i3-200001111000000000000
χ13222222-1-1-1-122-1-1-1-1222-1-1222222-1-1-1-12-122-1-1-1-1-1-1-1-1-1-1-1-2-200i3−i3i3−i300i3i3−i3−i300i3i3−i3−i3-200001111000000000000
χ142222-2-222222222-2-222222-2-2-2-222222222-2-2-2-2-2-2222-2-2-2-2-2-200000000000000000020000-2-222000000000000
χ152222-2-2-1-1-1-122-1-111222-1-1-2-2-2-222-1-1-1-12-1-2-21111-1-1-11111222-211-1-122-1-1-1-1-2-21111-20000-1-111000000000000
χ162222-2-2-1-1-1-122-1-111222-1-1-2-2-2-222-1-1-1-12-1-2-21111-1-1-1111122-22-1-111-2-2111122-1-1-1-1-20000-1-111000000000000
χ172222-2-2-1-1-1-122-1-111222-1-1-2-2-2-222-1-1-1-12-1-2-21111-1-1-11111-2-200−i3i3i3−i300i3i3−i3−i300−i3−i3i3i32000011-1-1000000000000
χ182222-2-2-1-1-1-122-1-111222-1-1-2-2-2-222-1-1-1-12-1-2-21111-1-1-11111-2-200i3−i3−i3i300−i3−i3i3i300i3i3−i3−i32000011-1-1000000000000
χ1922-2-22-222-2-222222-222-22222-2-2-2-2-2-2-2-2-222-222-2-22-2-222-2-200000000000000000000000000000000000002−22−2
χ2022-2-22-222-2-222222-222-22222-2-2-2-2-2-2-2-2-222-222-2-22-2-222-2-20000000000000000000000000000000000000−22−22
χ2122-2-2-2222-2-22222-2222-222-2-222-2-2-2-2-2-2-22-22-2-2222-2-2-2-22200000000000000000000000000000000000002−2−22
χ2222-2-2-2222-2-22222-2222-222-2-222-2-2-2-2-2-2-22-22-2-2222-2-2-2-2220000000000000000000000000000000000000−222−2
χ232-22-2002-2-22222200-2-22-2-200002-222-2-2-22000000-22-200002-20000000000000000000002i−2i2-20000002i2i−2i−2i0000
χ242-22-2002-2-22222200-2-22-2-200002-222-2-2-22000000-22-200002-2000000000000000000000−2i2i2-2000000−2i−2i2i2i0000
χ252-22-2002-2-22222200-2-22-2-200002-222-2-2-22000000-22-20000-2200000000000000000002i−2i00-22002i2i−2i−2i00000000
χ262-22-2002-2-22222200-2-22-2-200002-222-2-2-22000000-22-20000-220000000000000000000−2i2i00-2200−2i−2i2i2i00000000
χ2744444444441-211441-2-211-2-2-2-2111111-2-2111111-2-2-2-2-2-2-200222222-1-1-1-1-1-1-1-1-1-1-1-1000000000000000000000
χ2844444444441-211441-2-211-2-2-2-2111111-2-2111111-2-2-2-2-2-2-200-2-2-2-2-2-2111111111111000000000000000000000
χ294444444444-21-2-244-211-2-21111-2-2-2-2-2-211-2-2-2-2-2-2111111100000000000000000000022220000-1-1-1-1-1-1-1-10000
χ304444444444-21-2-244-211-2-21111-2-2-2-2-2-211-2-2-2-2-2-21111111000000000000000000000-2-2-2-20000111111110000
χ31444444-2-2-2-21-2−1−3i32−1+3i32-2-21-2-2−1−3i32−1+3i32-2-2-2-211−1−3i32−1+3i32−1−3i32−1+3i32-2111−1−3i32−1+3i32−1−3i32−1+3i3211111110022−1−i3−1+i3−1−i3−1+i3-1-11+i321+i321−i321−i32-1-11+i321+i321−i321−i32000000000000000000000
χ32444444-2-2-2-21-2−1−3i32−1+3i32-2-21-2-2−1−3i32−1+3i32-2-2-2-211−1−3i32−1+3i32−1−3i32−1+3i32-2111−1−3i32−1+3i32−1−3i32−1+3i32111111100-2-21+i31−i31+i31−i311−1−i32−1−i32−1+i32−1+i3211−1−i32−1−i32−1+i32−1+i32000000000000000000000
χ33444444-2-2-2-21-2−1+3i32−1−3i32-2-21-2-2−1+3i32−1−3i32-2-2-2-211−1+3i32−1−3i32−1+3i32−1−3i32-2111−1+3i32−1−3i32−1+3i32−1−3i3211111110022−1+i3−1−i3−1+i3−1−i3-1-11−i321−i321+i321+i32-1-11−i321−i321+i321+i32000000000000000000000
χ34444444-2-2-2-21-2−1+3i32−1−3i32-2-21-2-2−1+3i32−1−3i32-2-2-2-211−1+3i32−1−3i32−1+3i32−1−3i32-2111−1+3i32−1−3i32−1+3i32−1−3i32111111100-2-21−i31+i31−i31+i311−1+i32−1+i32−1−i32−1−i3211−1+i32−1+i32−1−i32−1−i32000000000000000000000
χ354444-4-444441-211-4-41-2-2112222111111-2-2-1-1-1-1-1-1-2-2-22222002-2-2-222-1-1-1-1-1-1111111000000000000000000000
χ364444-4-444441-211-4-41-2-2112222111111-2-2-1-1-1-1-1-1-2-2-2222200-2222-2-2111111-1-1-1-1-1-1000000000000000000000
χ374444-4-44444-21-2-2-4-4-211-2-2-1-1-1-1-2-2-2-2-2-211222222111-1-1-1-100000000000000000000022-2-20000-1-1-1-111110000
χ384444-4-44444-21-2-2-4-4-211-2-2-1-1-1-1-2-2-2-2-2-211222222111-1-1-1-1000000000000000000000-2-22200001111-1-1-1-10000
χ394444-4-4-2-2-2-21-2−1−3i32−1+3i32221-2-2−1−3i32−1+3i32222211−1−3i32−1+3i32−1−3i32−1+3i32-21-1-11+3i321−3i321+3i321−3i32111-1-1-1-1002-21+i31−i3−1−i3−1+i3-1-11+i321+i321−i321−i3211−1−i32−1−i32−1+i32−1+i32000000000000000000000
χ404444-4-4-2-2-2-21-2−1−3i32−1+3i32221-2-2−1−3i32−1+3i32222211−1−3i32−1+3i32−1−3i32−1+3i32-21-1-11+3i321−3i321+3i321−3i32111-1-1-1-100-22−1−i3−1+i31+i31−i311−1−i32−1−i32−1+i32−1+i32-1-11+i321+i321−i321−i32000000000000000000000
χ414444-4-4-2-2-2-21-2−1+3i32−1−3i32221-2-2−1+3i32−1−3i32222211−1+3i32−1−3i32−1+3i32−1−3i32-21-1-11−3i321+3i321−3i321+3i32111-1-1-1-1002-21−i31+i3−1+i3−1−i3-1-11−i321−i321+i321+i3211−1+i32−1+i32−1−i32−1−i32000000000000000000000
χ424444-4-4-2-2-2-21-2−1+3i32−1−3i32221-2-2−1+3i32−1−3i32222211−1+3i32−1−3i32−1+3i32−1−3i32-21-1-11−3i321+3i321−3i321+3i32111-1-1-1-100-22−1+i3−1−i31−i31+i311−1+i32−1+i32−1−i32−1−i32-1-11−i321−i321+i321+i32000000000000000000000
χ4344-4-44-444-4-41-2114-41-2211-2-222-1-1-1-1-1-12-21-111-1-1-222-2-222000000003−33−33−33−33−33−3000000000000000000000
χ4444-4-44-444-4-41-2114-41-2211-2-222-1-1-1-1-1-12-21-111-1-1-222-2-22200000000−33−33−33−33−33−33000000000000000000000
χ4544-4-44-444-4-4-21-2-24-4-21-1-2-211-1-1222222-11-22-2-2221-1-111-1-1000000000000000000000000000003−33−33−33−30000
χ4644-4-44-444-4-4-21-2-24-4-21-1-2-211-1-1222222-11-22-2-2221-1-111-1-100000000000000000000000000000−33−33−33−330000
χ4744-4-44-4-2-2221-2−1−3i32−1+3i32-221-22−1−3i32−1+3i32-2-222-1-11+3i321−3i321+3i321−3i32211-1−1−3i32−1+3i321+3i321−3i321-1-111-1-1000000003−32ζ14+ζ22−2ζ14−ζ22−ζ14−2ζ22ζ14+2ζ223−32ζ14+ζ22−2ζ14−ζ22−ζ14−2ζ22ζ14+2ζ22000000000000000000000
χ4844-4-44-4-2-2221-2−1−3i32−1+3i32-221-22−1−3i32−1+3i32-2-222-1-11+3i321−3i321+3i321−3i32211-1−1−3i32−1+3i321+3i321−3i321-1-111-1-100000000−33−2ζ14−ζ222ζ14+ζ22ζ14+2ζ22−ζ14−2ζ22−33−2ζ14−ζ222ζ14+ζ22ζ14+2ζ22−ζ14−2ζ22000000000000000000000
χ4944-4-44-4-2-2221-2−1+3i32−1−3i32-221-22−1+3i32−1−3i32-2-222-1-11−3i321+3i321−3i321+3i32211-1−1+3i32−1−3i321−3i321+3i321-1-111-1-1000000003−3−ζ14−2ζ22ζ14+2ζ222ζ14+ζ22−2ζ14−ζ223−3−ζ14−2ζ22ζ14+2ζ222ζ14+ζ22−2ζ14−ζ22000000000000000000000
χ5044-4-44-4-2-2221-2−1+3i32−1−3i32-221-22−1+3i32−1−3i32-2-222-1-11−3i321+3i321−3i321+3i32211-1−1+3i32−1−3i321−3i321+3i321-1-111-1-100000000−33ζ14+2ζ22−ζ14−2ζ22−2ζ14−ζ222ζ14+ζ22−33ζ14+2ζ22−ζ14−2ζ22−2ζ14−ζ222ζ14+ζ22000000000000000000000
χ5144-4-44-4-2-22244-2-2-2244-4-2-244-4-4-4-42222-4-24-4-2-222-222-2-22200000000000000000000000000000000000000000
χ5244-4-4-4444-4-41-211-441-221122-2-2-1-1-1-1-1-12-2-11-1-111-22222-2-2000000003−33−33−3−33−33−33000000000000000000000
χ5344-4-4-4444-4-41-211-441-221122-2-2-1-1-1-1-1-12-2-11-1-111-22222-2-200000000−33−33−333−33−33−3000000000000000000000
χ5444-4-4-4444-4-4-21-2-2-44-21-1-2-2-1-111222222-112-222-2-21-1-1-1-111000000000000000000000000000003−33−3−33−330000
χ5544-4-4-4444-4-4-21-2-2-44-21-1-2-2-1-111222222-112-222-2-21-1-1-1-11100000000000000000000000000000−33−333−33−30000
χ5644-4-4-44-2-2221-2−1−3i32−1+3i322-21-22−1−3i32−1+3i3222-2-2-1-11+3i321−3i321+3i321−3i3221-111+3i321−3i32−1−3i32−1+3i321-1-1-1-111000000003−32ζ14+ζ22−2ζ14−ζ22−ζ14−2ζ22ζ14+2ζ22−33−2ζ14−ζ222ζ14+ζ22ζ14+2ζ22−ζ14−2ζ22000000000000000000000
χ5744-4-4-44-2-2221-2−1−3i32−1+3i322-21-22−1−3i32−1+3i3222-2-2-1-11+3i321−3i321+3i321−3i3221-111+3i321−3i32−1−3i32−1+3i321-1-1-1-11100000000−33−2ζ14−ζ222ζ14+ζ22ζ14+2ζ22−ζ14−2ζ223−32ζ14+ζ22−2ζ14−ζ22−ζ14−2ζ22ζ14+2ζ22000000000000000000000
χ5844-4-4-44-2-2221-2−1+3i32−1−3i322-21-22−1+3i32−1−3i3222-2-2-1-11−3i321+3i321−3i321+3i3221-111−3i321+3i32−1+3i32−1−3i321-1-1-1-111000000003−3−ζ14−2ζ22ζ14+2ζ222ζ14+ζ22−2ζ14−ζ22−33ζ14+2ζ22−ζ14−2ζ22−2ζ14−ζ222ζ14+ζ22000000000000000000000
χ5944-4-4-44-2-2221-2−1+3i32−1−3i322-21-22−1+3i32−1−3i3222-2-2-1-11−3i321+3i321−3i321+3i3221-111−3i321+3i32−1+3i32−1−3i321-1-1-1-11100000000−33ζ14+2ζ22−ζ14−2ζ22−2ζ14−ζ222ζ14+ζ223−3−ζ14−2ζ22ζ14+2ζ222ζ14+ζ22−2ζ14−ζ22000000000000000000000
χ6044-4-4-44-2-22244-2-22-244-4-2-2-4-444-4-42222-4-2-4422-2-2-22222-2-200000000000000000000000000000000000000000
χ614-44-4004-4-44-21-2-2002-11223-33-3-22-2-222-11000000-11-13-33-30000000000000000000002i−2i2i−2i0000−i−iii−i−iii0000
χ624-44-4004-4-44-21-2-2002-11223-33-3-22-2-222-11000000-11-13-33-3000000000000000000000−2i2i−2i2i0000ii−i−iii−i−i0000
χ634-44-4004-4-44-21-2-2002-1122-33-33-22-2-222-11000000-11-1-33-330000000000000000000002i−2i−2i2i0000−i−iiiii−i−i0000
χ644-44-4004-4-44-21-2-2002-1122-33-33-22-2-222-11000000-11-1-33-33000000000000000000000−2i2i2i−2i0000ii−i−i−i−iii0000
χ654-44-400-222-244-2-200-4-442200004-4-2-222-4-20000002-2200004-400000000000000000000000-2200000000000000
χ664-44-400-222-244-2-200-4-442200004-4-2-222-4-20000002-220000-44000000000000000000000002-200000000000000
χ674-4-44004-44-4444400-4-4-4-4-40000-44-4-44444000000-4-44000000000000000000000000000000000000000000000
χ684-4-44004-44-4-21-2-2002-1-1223-3-332-222-2-211000000-1-113-3-3300000000000000000000000000000−i3i3i3−i3−i3i3i3−i30000
χ694-4-44004-44-4-21-2-2002-1-1223-3-332-222-2-211000000-1-113-3-3300000000000000000000000000000i3−i3−i3i3i3−i3−i3i30000
χ704-4-44004-44-4-21-2-2002-1-122-333-32-222-2-211000000-1-11-333-300000000000000000000000000000−i3i3i3−i3i3−i3−i3i30000
χ714-4-44004-44-4-21-2-2002-1-122-333-32-222-2-211000000-1-11-333-300000000000000000000000000000i3−i3−i3i3−i3i3i3−i30000
χ724-4-4400-22-2244-2-200-4-4-4220000-4422-2-24-200000022-2000000000000000000000000000000023−23000000000000
χ734-4-4400-22-2244-2-200-4-4-4220000-4422-2-24-200000022-20000000000000000000000000000000−2323000000000000
χ74888888-4-4-4-4-4222-4-4-422222222-4-422222-1-4-42222-1-1-1-1-1-1-100000000000000000000000000000000000000000
χ758888-8-8-4-4-4-4-422244-42222-2-2-2-2-4-422222-144-2-2-2-2-1-1-1111100000000000000000000000000000000000000000
χ7688-8-88-8-4-444-4222-44-42-22222-2-244-2-2-2-2-2-1-4422-2-2-111-1-11100000000000000000000000000000000000000000
χ7788-8-8-88-4-444-42224-4-42-222-2-22244-2-2-2-2-2-14-4-2-222-11111-1-100000000000000000000000000000000000000000
χ788-88-8008-8-882-42200-24-4-2-200002-222-2-24-40000004-44000000000000000000000000000000000000000000000
χ798-88-800-444-42-4−1−3i3−1+3i300-24-41+3i31−3i300002-2−1−3i3−1+3i31+3i31−3i342000000-22-2000000000000000000000000000000000000000000000
χ808-88-800-444-42-4−1+3i3−1−3i300-24-41−3i31+3i300002-2−1+3i3−1−3i31−3i31+3i342000000-22-2000000000000000000000000000000000000000000000
χ818-88-800-444-4-4222004-22-2-26-66-6-4422-2-2-2-10000001-11-33-3300000000000000000000000000000000000000000
χ828-88-800-444-4-4222004-22-2-2-66-66-4422-2-2-2-10000001-113-33-300000000000000000000000000000000000000000
χ838-8-88008-88-82-42200-244-2-20000-22-2-222-4-400000044-4000000000000000000000000000000000000000000000
χ848-8-8800-44-442-4−1−3i3−1+3i300-2441+3i31−3i30000-221+3i31−3i3−1−3i3−1+3i3-42000000-2-22000000000000000000000000000000000000000000000
χ858-8-8800-44-442-4−1+3i3−1−3i300-2441−3i31+3i30000-221−3i31+3i3−1+3i3−1−3i3-42000000-2-22000000000000000000000000000000000000000000000
χ868-8-8800-44-44-4222004-2-2-2-26-6-664-4-2-2222-100000011-1-333-300000000000000000000000000000000000000000
χ878-8-8800-44-44-4222004-2-2-2-2-666-64-4-2-2222-100000011-13-3-3300000000000000000000000000000000000000000

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