Finite Group Databasebeta

← Group #13167280

Character table — Group #13167280

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87
size111122222244444444444444444444448888888888888818182424242424242424242424242424242424243636363636363636363636363636363636108108108108
order12222236663333666666666666666666366666666666664424666666661212121212121212444441212121212121212121212128888
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
χ51111-1-111111111-1-111-1-1-1-111111111111-1-1-1-1-1-1111-1-1-1-1111-111111111-1-1-1-1-1-1-1-1-111-1-111-1-11111-1-1-1-111-1-1
χ61111-1-111111111-1-111-1-1-1-111111111111-1-1-1-1-1-1111-1-1-1-1111-111111111-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111-1-111
χ71111-1-111111111-1-111-1-1-1-111111111111-1-1-1-1-1-1111-1-1-1-111-11-1-1-1-1-1-1-1-111111111-111-1-111-1-11111-1-1-1-1-1-111
χ81111-1-111111111-1-111-1-1-1-111111111111-1-1-1-1-1-1111-1-1-1-111-11-1-1-1-1-1-1-1-111111111-1-1-11111-1-1-1-1-1-1111111-1-1
χ92222222222222222222222222222222222222222222222-2-2000000000000000000-20000-2-2-2-2000000000000
χ10222222-1-1-1-122-1-1-1-122222222-1-1-1-12-1-12-122-1-1-1-1-1-1-1-1-1-1-12222-1-122-1-1-1-1-1-122-1-1-1-120000-1-1-1-1000000000000
χ11222222-1-1-1-122-1-1-1-122222222-1-1-1-12-1-12-122-1-1-1-1-1-1-1-1-1-1-122-2-211-2-2111111-2-2111120000-1-1-1-1000000000000
χ12222222-1-1-1-122-1-1-1-122222222-1-1-1-12-1-12-122-1-1-1-1-1-1-1-1-1-1-1-2-200−i3i300−i3−i3i3i3−i3i300−i3−i3i3i3-200001111000000000000
χ13222222-1-1-1-122-1-1-1-122222222-1-1-1-12-1-12-122-1-1-1-1-1-1-1-1-1-1-1-2-200i3−i300i3i3−i3−i3i3−i300i3i3−i3−i3-200001111000000000000
χ142222-2-222222222-2-222-2-2-2-222222222222-2-2-2-2-2-2222-2-2-2-2-2-200000000000000000020000-2-222000000000000
χ152222-2-2-1-1-1-122-1-11122-2-2-2-222-1-1-1-12-1-12-1-2-21111-1-1-11111222-2-1-122-1-1-1-111-2-21111-20000-1-111000000000000
χ162222-2-2-1-1-1-122-1-11122-2-2-2-222-1-1-1-12-1-12-1-2-21111-1-1-1111122-2211-2-21111-1-122-1-1-1-1-20000-1-111000000000000
χ172222-2-2-1-1-1-122-1-11122-2-2-2-222-1-1-1-12-1-12-1-2-21111-1-1-11111-2-200−i3i300−i3−i3i3i3i3−i300i3i3−i3−i32000011-1-1000000000000
χ182222-2-2-1-1-1-122-1-11122-2-2-2-222-1-1-1-12-1-12-1-2-21111-1-1-11111-2-200i3−i300i3i3−i3−i3−i3i300−i3−i3i3i32000011-1-1000000000000
χ192-22-2002-2-222222002-200002-222-2-2-2-2-2-220000002-2-200002-20000000000000000000002i−2i2-20000002i2i−2i−2i0000
χ202-22-2002-2-222222002-200002-222-2-2-2-2-2-220000002-2-200002-2000000000000000000000−2i2i2-2000000−2i−2i2i2i0000
χ212-22-2002-2-222222002-200002-222-2-2-2-2-2-220000002-2-20000-2200000000000000000002i−2i00-22002i2i−2i−2i00000000
χ222-22-2002-2-222222002-200002-222-2-2-2-2-2-220000002-2-20000-220000000000000000000−2i2i00-2200−2i−2i2i2i00000000
χ232-2-222-22-22-222222-2-2-222-2-2-2-2-2-2-2-2222222-222-2-2-22-222-2-200000000000000000000000000000000000002−22−2
χ242-2-222-22-22-222222-2-2-222-2-2-2-2-2-2-2-2222222-222-2-2-22-222-2-20000000000000000000000000000000000000−22−22
χ252-2-22-222-22-22222-22-2-2-2-222-2-2-2-2-2-222222-22-2-222-22-2-2-22200000000000000000000000000000000000002−2−22
χ262-2-22-222-22-22222-22-2-2-2-222-2-2-2-2-2-222222-22-2-222-22-2-2-2220000000000000000000000000000000000000−222−2
χ2744444444441-2-2-244111111-2-2-2-2-2-2-2-2-211-2-2-2-2-2-2111111100000000000000000000022220000-1-1-1-1-1-1-1-10000
χ2844444444441-2-2-244111111-2-2-2-2-2-2-2-2-211-2-2-2-2-2-21111111000000000000000000000-2-2-2-20000111111110000
χ294444444444-211144-2-2-2-2-2-2111111111-2-2111111-2-2-2-2-2-2-2002222-1-1-1-1-1-122-1-1-1-1-1-1000000000000000000000
χ304444444444-211144-2-2-2-2-2-2111111111-2-2111111-2-2-2-2-2-2-200-2-2-2-2111111-2-2111111000000000000000000000
χ31444444-2-2-2-2-21−1−3i32−1+3i32-2-2-2-2-2-2-2-211−1−3i32−1+3i32−1−3i32−1+3i321−1−3i32−1+3i32-2111−1−3i32−1+3i32−1−3i32−1+3i3211111110022−1−i3−1+i3-1-11+i321+i321−i321−i32−1−i3−1+i3-1-11+i321+i321−i321−i32000000000000000000000
χ32444444-2-2-2-2-21−1−3i32−1+3i32-2-2-2-2-2-2-2-211−1−3i32−1+3i32−1−3i32−1+3i321−1−3i32−1+3i32-2111−1−3i32−1+3i32−1−3i32−1+3i32111111100-2-21+i31−i311−1−i32−1−i32−1+i32−1+i321+i31−i311−1−i32−1−i32−1+i32−1+i32000000000000000000000
χ33444444-2-2-2-2-21−1+3i32−1−3i32-2-2-2-2-2-2-2-211−1+3i32−1−3i32−1+3i32−1−3i321−1+3i32−1−3i32-2111−1+3i32−1−3i32−1+3i32−1−3i3211111110022−1+i3−1−i3-1-11−i321−i321+i321+i32−1+i3−1−i3-1-11−i321−i321+i321+i32000000000000000000000
χ34444444-2-2-2-2-21−1+3i32−1−3i32-2-2-2-2-2-2-2-211−1+3i32−1−3i32−1+3i32−1−3i321−1+3i32−1−3i32-2111−1+3i32−1−3i32−1+3i32−1−3i32111111100-2-21−i31+i311−1+i32−1+i32−1−i32−1−i321−i31+i311−1+i32−1+i32−1−i32−1−i32000000000000000000000
χ354444-4-444441-2-2-2-4-411-1-1-1-1-2-2-2-2-2-2-2-2-211222222111-1-1-1-100000000000000000000022-2-20000-1-1-1-111110000
χ364444-4-444441-2-2-2-4-411-1-1-1-1-2-2-2-2-2-2-2-2-211222222111-1-1-1-1000000000000000000000-2-22200001111-1-1-1-10000
χ374444-4-44444-2111-4-4-2-22222111111111-2-2-1-1-1-1-1-1-2-2-22222002-222-1-1-1-1-1-1-2-2111111000000000000000000000
χ384444-4-44444-2111-4-4-2-22222111111111-2-2-1-1-1-1-1-1-2-2-2222200-22-2-211111122-1-1-1-1-1-1000000000000000000000
χ394444-4-4-2-2-2-2-21−1−3i32−1+3i3222-2-2222211−1−3i32−1+3i32−1−3i32−1+3i321−1−3i32−1+3i32-21-1-11+3i321−3i321+3i321−3i32111-1-1-1-1002-2−1−i3−1+i3-1-11+i321+i321−i321−i321+i31−i311−1−i32−1−i32−1+i32−1+i32000000000000000000000
χ404444-4-4-2-2-2-2-21−1−3i32−1+3i3222-2-2222211−1−3i32−1+3i32−1−3i32−1+3i321−1−3i32−1+3i32-21-1-11+3i321−3i321+3i321−3i32111-1-1-1-100-221+i31−i311−1−i32−1−i32−1+i32−1+i32−1−i3−1+i3-1-11+i321+i321−i321−i32000000000000000000000
χ414444-4-4-2-2-2-2-21−1+3i32−1−3i3222-2-2222211−1+3i32−1−3i32−1+3i32−1−3i321−1+3i32−1−3i32-21-1-11−3i321+3i321−3i321+3i32111-1-1-1-1002-2−1+i3−1−i3-1-11−i321−i321+i321+i321−i31+i311−1+i32−1+i32−1−i32−1−i32000000000000000000000
χ424444-4-4-2-2-2-2-21−1+3i32−1−3i3222-2-2222211−1+3i32−1−3i32−1+3i32−1−3i321−1+3i32−1−3i32-21-1-11−3i321+3i321−3i321+3i32111-1-1-1-100-221−i31+i311−1+i32−1+i32−1−i32−1−i32−1+i3−1−i3-1-11−i321−i321+i321+i32000000000000000000000
χ4344-4-40044-4-41-2-2-200-113-33-32-222-2-2222-11000000-1-113-33-3000000000000000000000000000003−33−33−33−30000
χ4444-4-40044-4-41-2-2-200-113-33-32-222-2-2222-11000000-1-113-33-300000000000000000000000000000−33−33−33−330000
χ4544-4-40044-4-41-2-2-200-11-33-332-222-2-2222-11000000-1-11-33-33000000000000000000000000000003−33−3−33−330000
χ4644-4-40044-4-41-2-2-200-11-33-332-222-2-2222-11000000-1-11-33-3300000000000000000000000000000−33−333−33−30000
χ4744-4-40044-4-4444400-440000-44-4-444-4-4-4-44000000-4-44000000000000000000000000000000000000000000000
χ4844-4-400-2-22244-2-200-440000-4422-2-2-422-4-200000022-2000000000000000000000000000000023−23000000000000
χ4944-4-400-2-22244-2-200-440000-4422-2-2-422-4-200000022-20000000000000000000000000000000−2323000000000000
χ504-44-4004-4-441-2-2-2001-13-3-33-22-2-222222-110000001-1-13-3-330000000000000000000002i−2i2i−2i0000−i−iii−i−iii0000
χ514-44-4004-4-441-2-2-2001-13-3-33-22-2-222222-110000001-1-13-3-33000000000000000000000−2i2i−2i2i0000ii−i−iii−i−i0000
χ524-44-4004-4-441-2-2-2001-1-333-3-22-2-222222-110000001-1-1-333-30000000000000000000002i−2i−2i2i0000−i−iiiii−i−i0000
χ534-44-4004-4-441-2-2-2001-1-333-3-22-2-222222-110000001-1-1-333-3000000000000000000000−2i2i2i−2i0000ii−i−i−i−iii0000
χ544-44-400-222-244-2-2004-400004-4-2-222-422-4-2000000-22200004-400000000000000000000000-2200000000000000
χ554-44-400-222-244-2-2004-400004-4-2-222-422-4-2000000-2220000-44000000000000000000000002-200000000000000
χ564-4-444-44-44-41-2-2-24-4-1-111-1-1222222-2-2-211-22-2-222-11-111-1-100000000000000000000000000000−i3i3i3−i3−i3i3i3−i30000
χ574-4-444-44-44-41-2-2-24-4-1-111-1-1222222-2-2-211-22-2-222-11-111-1-100000000000000000000000000000i3−i3−i3i3i3−i3−i3i30000
χ584-4-444-44-44-4-21114-422-2-222-1-1-1-1-1-1111-2-21-111-1-12-22-2-222000000−i3i3−i3i3−i3i300−i3i3−i3i3−i3i3000000000000000000000
χ594-4-444-44-44-4-21114-422-2-222-1-1-1-1-1-1111-2-21-111-1-12-22-2-222000000i3−i3i3−i3i3−i300i3−i3i3−i3i3−i3000000000000000000000
χ604-4-444-4-22-2244-2-2-22-4-444-4-4-4-422224-2-24-24-4-2-2222-22-2-22200000000000000000000000000000000000000000
χ614-4-444-4-22-22-21−1−3i32−1+3i32-2222-2-222-1-11+3i321−3i321+3i321−3i321−1−3i32−1+3i32-211-1−1−3i32−1+3i321+3i321−3i32-11-111-1-1000000−i3i3−3+i323−i323+i32−3−i3200−i3i3−3+i323−i323+i32−3−i32000000000000000000000
χ624-4-444-4-22-22-21−1−3i32−1+3i32-2222-2-222-1-11+3i321−3i321+3i321−3i321−1−3i32−1+3i32-211-1−1−3i32−1+3i321+3i321−3i32-11-111-1-1000000i3−i33−i32−3+i32−3−i323+i3200i3−i33−i32−3+i32−3−i323+i32000000000000000000000
χ634-4-444-4-22-22-21−1+3i32−1−3i32-2222-2-222-1-11−3i321+3i321−3i321+3i321−1+3i32−1−3i32-211-1−1+3i32−1−3i321−3i321+3i32-11-111-1-1000000−i3i33+i32−3−i32−3+i323−i3200−i3i33+i32−3−i32−3+i323−i32000000000000000000000
χ644-4-444-4-22-22-21−1+3i32−1−3i32-2222-2-222-1-11−3i321+3i321−3i321+3i321−1+3i32−1−3i32-211-1−1+3i32−1−3i321−3i321+3i32-11-111-1-1000000i3−i3−3−i323+i323−i32−3+i3200i3−i3−3−i323+i323−i32−3+i32000000000000000000000
χ654-4-44-444-44-41-2-2-2-44-1-1-1-111222222-2-2-2112-222-2-2-11-1-1-11100000000000000000000000000000−i3i3i3−i3i3−i3−i3i30000
χ664-4-44-444-44-41-2-2-2-44-1-1-1-111222222-2-2-2112-222-2-2-11-1-1-11100000000000000000000000000000i3−i3−i3i3−i3i3i3−i30000
χ674-4-44-444-44-4-2111-442222-2-2-1-1-1-1-1-1111-2-2-11-1-1112-2222-2-2000000−i3i3−i3i3−i3i300i3−i3i3−i3i3−i3000000000000000000000
χ684-4-44-444-44-4-2111-442222-2-2-1-1-1-1-1-1111-2-2-11-1-1112-2222-2-2000000i3−i3i3−i3i3−i300−i3i3−i3i3−i3i3000000000000000000000
χ694-4-44-44-22-2244-2-22-2-4-4-4-444-4-422224-2-24-2-4422-2-22-2222-2-200000000000000000000000000000000000000000
χ704-4-44-44-22-22-21−1−3i32−1+3i322-22222-2-2-1-11+3i321−3i321+3i321−3i321−1−3i32−1+3i32-21-111+3i321−3i32−1−3i32−1+3i32-11-1-1-111000000−i3i3−3+i323−i323+i32−3−i3200i3−i33−i32−3+i32−3−i323+i32000000000000000000000
χ714-4-44-44-22-22-21−1−3i32−1+3i322-22222-2-2-1-11+3i321−3i321+3i321−3i321−1−3i32−1+3i32-21-111+3i321−3i32−1−3i32−1+3i32-11-1-1-111000000i3−i33−i32−3+i32−3−i323+i3200−i3i3−3+i323−i323+i32−3−i32000000000000000000000
χ724-4-44-44-22-22-21−1+3i32−1−3i322-22222-2-2-1-11−3i321+3i321−3i321+3i321−1+3i32−1−3i32-21-111−3i321+3i32−1+3i32−1−3i32-11-1-1-111000000−i3i33+i32−3−i32−3+i323−i3200i3−i3−3−i323+i323−i32−3+i32000000000000000000000
χ734-4-44-44-22-22-21−1+3i32−1−3i322-22222-2-2-1-11−3i321+3i321−3i321+3i321−1+3i32−1−3i32-21-111−3i321+3i32−1+3i32−1−3i32-11-1-1-111000000i3−i3−3−i323+i323−i32−3+i3200−i3i33+i32−3−i32−3+i323−i32000000000000000000000
χ74888888-4-4-4-42-422-4-4222222-4-42222-4222-1-4-42222-1-1-1-1-1-1-100000000000000000000000000000000000000000
χ758888-8-8-4-4-4-42-4224422-2-2-2-2-4-42222-4222-144-2-2-2-2-1-1-1111100000000000000000000000000000000000000000
χ7688-8-80088-8-8-4222004-40000-22-2-222-2-2-24-400000044-4000000000000000000000000000000000000000000000
χ7788-8-800-4-4442-42200-226-66-64-4-2-2224-2-2-2-100000011-1-33-3300000000000000000000000000000000000000000
χ7888-8-800-4-4442-42200-22-66-664-4-2-2224-2-2-2-100000011-13-33-300000000000000000000000000000000000000000
χ7988-8-800-4-444-42−1−3i3−1+3i3004-40000-221+3i31−3i3−1−3i3−1+3i3-21+3i31−3i342000000-2-22000000000000000000000000000000000000000000000
χ8088-8-800-4-444-42−1+3i3−1−3i3004-40000-221−3i31+3i3−1+3i3−1−3i3-21−3i31+3i342000000-2-22000000000000000000000000000000000000000000000
χ818-88-8008-8-88-422200-4400002-222-2-2-2-2-24-4000000-444000000000000000000000000000000000000000000000
χ828-88-800-444-42-422002-26-6-66-4422-2-24-2-2-2-1000000-111-333-300000000000000000000000000000000000000000
χ838-88-800-444-42-422002-2-666-6-4422-2-24-2-2-2-1000000-1113-3-3300000000000000000000000000000000000000000
χ848-88-800-444-4-42−1−3i3−1+3i300-4400002-2−1−3i3−1+3i31+3i31−3i3-21+3i31−3i3420000002-2-2000000000000000000000000000000000000000000000
χ858-88-800-444-4-42−1+3i3−1−3i300-4400002-2−1+3i3−1−3i31−3i31+3i3-21−3i31+3i3420000002-2-2000000000000000000000000000000000000000000000
χ868-8-888-8-44-442-422-44-2-222-2-244-2-2-2-2-4222-1-4422-2-21-11-1-11100000000000000000000000000000000000000000
χ878-8-88-88-44-442-4224-4-2-2-2-22244-2-2-2-2-4222-14-4-2-2221-1111-1-100000000000000000000000000000000000000000

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