Finite Group Databasebeta

← Group #13138832

Character table — Group #13138832

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83
size1111222222444444446666666666661212121212121212121212121212121212121212121212121212181836363636363636363636363636363672727272727272727272
order1222344666881212242424243366666612121212366612121212121224242424242424242424242424242424224444466881212242424242466121212121212
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111111111111111-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11-111-1-1-1-111
χ411111111111111111111111111111111111111111111111111111111-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-11-1-11111-1-1
χ51111111111-1-111-1-1-1-11111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111-1-111-1-1-1-1-1-1-1-111-1-111
χ61111111111-1-111-1-1-1-11111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111-1-1-1-111-1-111-1-1-1-11111-1-111-1-1
χ71111111111-1-111-1-1-1-11111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111-1-11111-11-1-1-1-11111
χ81111111111-1-111-1-1-1-11111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-111111-11111-1-1-1-1
χ92222222222222222222-122-1-12-12222-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-10002200000000000020-1-10000-1-1
χ102222222222222222222-122-1-12-12222-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1000-2-2000000000000-2011000011
χ11222222222222222222-12-1-122-12-1-1-1-1-1-1-1-12-1-12-1-1-1-1-1-12222-1-1-1-1-1-1-1-12220000-1-122-1-1-1-1-1-10000000000
χ12222222222222222222-12-1-122-12-1-1-1-1-1-1-1-12-1-12-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-2-2-2000011-2-21111110000000000
χ132222222222-2-222-2-2-2-22-122-1-12-12222-1-1-1-1-1-1-1-1-1-1-2-2-2-211111111111100022000000000000-20110000-1-1
χ142222222222-2-222-2-2-2-22-122-1-12-12222-1-1-1-1-1-1-1-1-1-1-2-2-2-2111111111111000-2-200000000000020-1-1000011
χ152222222222-2-222-2-2-2-2-12-1-122-12-1-1-1-1-1-1-1-12-1-12-1-11111-2-2-2-2111111112220000-1-1-2-2-1-111110000000000
χ162222222222-2-222-2-2-2-2-12-1-122-12-1-1-1-1-1-1-1-12-1-12-1-11111-2-2-2-211111111-2-2-20000112211-1-1-1-10000000000
χ1722222-2-222200-2-2000022222222-2-2-2-22222-2-2-2-2-2-2000000000000000022-200002200-2-200000000000000
χ1822222-2-222200-2-2000022222222-2-2-2-22222-2-2-2-2-2-20000000000000000-2-220000-2-2002200000000000000
χ1922222-2-222200-2-20000-12-1-122-121111-1-1-1-1-211-21133−3−300003333−3−3−3−322-20000-1-1001133−3−30000000000
χ2022222-2-222200-2-20000-12-1-122-121111-1-1-1-1-211-21133−3−300003333−3−3−3−3-2-2200001100-1-1−3−3330000000000
χ2122222-2-222200-2-20000-12-1-122-121111-1-1-1-1-211-211−3−3330000−3−3−3−3333322-20000-1-10011−3−3330000000000
χ2222222-2-222200-2-20000-12-1-122-121111-1-1-1-1-211-211−3−3330000−3−3−3−33333-2-2200001100-1-133−3−30000000000
χ232-22-222-2-22-200-22000022-2-2-222-222-2-22-2-22-2-2-22220000000000000000000002i−2i000000000000002i−2i0000
χ242-22-222-2-22-200-22000022-2-2-222-222-2-22-2-22-2-2-2222000000000000000000000−2i2i00000000000000−2i2i0000
χ252-22-22-22-22-2002-2000022-2-2-222-2-2-2222-2-22222-2-2-200000000000000000002i−2i000000000000000000002i−2i
χ262-22-22-22-22-2002-2000022-2-2-222-2-2-2222-2-22222-2-2-20000000000000000000−2i2i00000000000000000000−2i2i
χ272-22-22-22-22-2002-200002-1-2-21-121-2-222-111-1-1-1-1111000033−3−333−3−333−3−30002i−2i00000000000000−i3i30000−ii
χ282-22-22-22-22-2002-200002-1-2-21-121-2-222-111-1-1-1-1111000033−3−333−3−333−3−3000−2i2i00000000000000i3−i30000i−i
χ292-22-22-22-22-2002-200002-1-2-21-121-2-222-111-1-1-1-11110000−3−333−3−333−3−3330002i−2i00000000000000i3−i30000−ii
χ302-22-22-22-22-2002-200002-1-2-21-121-2-222-111-1-1-1-11110000−3−333−3−333−3−333000−2i2i00000000000000−i3i30000i−i
χ312-2-22200-2-222−20022−2−2222-2-2-2-22000022-2-20000002−22−22−22−22−22−22−22−22-2000002-22−2002−22−20000000000
χ322-2-22200-2-222−20022−2−2222-2-2-2-22000022-2-20000002−22−22−22−22−22−22−22−2-2200000-22−2200−22−220000000000
χ332-2-22200-2-222−20022−2−2-12-11-2-2123−33−3-1-11103−303−3ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ232−22−2ζ5−ζ7−ζ5+ζ7ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23ζ13−ζ23−ζ13+ζ232-200000-112−23−3ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ230000000000
χ342-2-22200-2-222−20022−2−2-12-11-2-2123−33−3-1-11103−303−3ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ232−22−2ζ5−ζ7−ζ5+ζ7ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23ζ13−ζ23−ζ13+ζ23-22000001-1−22−33−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ230000000000
χ352-2-22200-2-222−20022−2−2-12-11-2-212−33−33-1-1110−330−33ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ72−22−2ζ13−ζ23−ζ13+ζ23ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7ζ5−ζ7−ζ5+ζ72-200000-112−2−33ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ70000000000
χ362-2-22200-2-222−20022−2−2-12-11-2-212−33−33-1-1110−330−33ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ72−22−2ζ13−ζ23−ζ13+ζ23ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7ζ5−ζ7−ζ5+ζ7-22000001-1−223−3−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ70000000000
χ372-2-22200-2-22−2200−2−222222-2-2-2-22000022-2-2000000−22−22−22−22−22−22−22−222-2000002-2−2200−22−220000000000
χ382-2-22200-2-22−2200−2−222222-2-2-2-22000022-2-2000000−22−22−22−22−22−22−22−22-2200000-222−2002−22−20000000000
χ392-2-22200-2-22−2200−2−222-12-11-2-2123−33−3-1-11103−303−3−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23−22−22−ζ5+ζ7ζ5−ζ7−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23−ζ13+ζ23ζ13−ζ232-200000-11−223−3−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ230000000000
χ402-2-22200-2-22−2200−2−222-12-11-2-2123−33−3-1-11103−303−3−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23−22−22−ζ5+ζ7ζ5−ζ7−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23−ζ13+ζ23ζ13−ζ23-22000001-12−2−33ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ230000000000
χ412-2-22200-2-22−2200−2−222-12-11-2-212−33−33-1-1110−330−33−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7−22−22−ζ13+ζ23ζ13−ζ23−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7−ζ5+ζ7ζ5−ζ72-200000-11−22−33−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ70000000000
χ422-2-22200-2-22−2200−2−222-12-11-2-212−33−33-1-1110−330−33−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7−22−22−ζ13+ζ23ζ13−ζ23−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7−ζ5+ζ7ζ5−ζ7-22000001-12−23−3ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ70000000000
χ43444444444444444444-2-2-2-2-2-2-2-2-2-2-2-21111-211-211-2-2-2-2-2-2-2-211111111000000000000000000000000000
χ444444444444-4-444-4-4-4-4-2-2-2-2-2-2-2-2-2-2-2-21111-211-21122222222-1-1-1-1-1-1-1-1000000000000000000000000000
χ4544444-4-444400-4-400004-244-2-24-2-4-4-4-4-2-2-2-22222220000000000000000000000000000000000000000000
χ4644444-4-444400-4-40000-2-2-2-2-2-2-2-2222211112-1-12-1-12323−23−230000−3−3−3−33333000000000000000000000000000
χ4744444-4-444400-4-40000-2-2-2-2-2-2-2-2222211112-1-12-1-1−23−23232300003333−3−3−3−3000000000000000000000000000
χ4844-4-44004-4-40000000044-444-4-4-400004-44-40000000000000000000000000000000000000000000000000
χ4944-4-44004-4-4000000004-2-44-22-420000-22-2200000000006−6−666−6−666−6−66000000000000000000000000000
χ5044-4-44004-4-4000000004-2-44-22-420000-22-220000000000−666−6−666−6−666−6000000000000000000000000000
χ5144-4-44004-4-400000000-242-24-42-423−23−2323-22-220−2323023−230000000000000000000000000000000000000000000
χ5244-4-44004-4-400000000-242-24-42-4−232323−23-22-22023−230−23230000000000000000000000000000000000000000000
χ5344-4-44004-4-400000000-2-22-2-222223−23−23231-11-103−30−3300006−6−66ζ5−ζ7+2ζ13−2ζ23−ζ5+ζ7−2ζ13+2ζ23−ζ5+ζ7−2ζ13+2ζ23ζ5−ζ7+2ζ13−2ζ23−2ζ5+2ζ7−ζ13+ζ232ζ5−2ζ7+ζ13−ζ232ζ5−2ζ7+ζ13−ζ23−2ζ5+2ζ7−ζ13+ζ23000000000000000000000000000
χ5444-4-44004-4-400000000-2-22-2-222223−23−23231-11-103−30−330000−666−6−ζ5+ζ7−2ζ13+2ζ23ζ5−ζ7+2ζ13−2ζ23ζ5−ζ7+2ζ13−2ζ23−ζ5+ζ7−2ζ13+2ζ232ζ5−2ζ7+ζ13−ζ23−2ζ5+2ζ7−ζ13+ζ23−2ζ5+2ζ7−ζ13+ζ232ζ5−2ζ7+ζ13−ζ23000000000000000000000000000
χ5544-4-44004-4-400000000-2-22-2-2222−232323−231-11-10−3303−300006−6−66−2ζ5+2ζ7−ζ13+ζ232ζ5−2ζ7+ζ13−ζ232ζ5−2ζ7+ζ13−ζ23−2ζ5+2ζ7−ζ13+ζ23ζ5−ζ7+2ζ13−2ζ23−ζ5+ζ7−2ζ13+2ζ23−ζ5+ζ7−2ζ13+2ζ23ζ5−ζ7+2ζ13−2ζ23000000000000000000000000000
χ5644-4-44004-4-400000000-2-22-2-2222−232323−231-11-10−3303−30000−666−62ζ5−2ζ7+ζ13−ζ23−2ζ5+2ζ7−ζ13+ζ23−2ζ5+2ζ7−ζ13+ζ232ζ5−2ζ7+ζ13−ζ23−ζ5+ζ7−2ζ13+2ζ23ζ5−ζ7+2ζ13−2ζ23ζ5−ζ7+2ζ13−2ζ23−ζ5+ζ7−2ζ13+2ζ23000000000000000000000000000
χ574-44-444-4-44-400-4400004-2-4-42-24244-4-4-222-2222-2-2-20000000000000000000000000000000000000000000
χ584-44-444-4-44-400-440000-2422-44-2-4-2-222-222-2-4224-2-20000000000000000000000000000000000000000000
χ594-44-444-4-44-400-440000-2-2222-2-22-2-2221-1-112-1-1-2110000000033-3-3-3-333000000000000000000000000000
χ604-44-444-4-44-400-440000-2-2222-2-22-2-2221-1-112-1-1-21100000000-3-33333-3-3000000000000000000000000000
χ614-44-44-44-44-4004-40000-2422-44-2-422-2-2-222-24-2-2-4220000000000000000000000000000000000000000000
χ624-44-44-44-44-4004-40000-2-2222-2-2222-2-21-1-11-2112-1-100002323−23−23−3−333−3−333000000000000000000000000000
χ634-44-44-44-44-4004-40000-2-2222-2-2222-2-21-1-11-2112-1-10000−23−23232333−3−333−3−3000000000000000000000000000
χ644-4-44400-4-4422−22002222−22−224-24-422-4-20000-2-22200000022−2222−22−22−22−22−22−22−22000000000000000000000000000
χ654-4-44400-4-4422−22002222−22−22-2-2-22222-223−2323−2311-1-10−330−332ζ5−2ζ7−2ζ5+2ζ72ζ13−2ζ23−2ζ13+2ζ23−22−22−ζ5+ζ7ζ5−ζ7−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23−ζ13+ζ23ζ13−ζ23000000000000000000000000000
χ664-4-44400-4-4422−22002222−22−22-2-2-22222-2−2323−232311-1-103−303−32ζ13−2ζ23−2ζ13+2ζ232ζ5−2ζ7−2ζ5+2ζ7−22−22−ζ13+ζ23ζ13−ζ23−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7−ζ5+ζ7ζ5−ζ7000000000000000000000000000
χ674-4-44400-4-44−222200−22−2222224-24-422-4-20000-2-222000000−2222−22222−22−22−22−22−22−2000000000000000000000000000
χ684-4-44400-4-44−222200−22−222222-2-2-22222-223−2323−2311-1-10−330−33−2ζ5+2ζ72ζ5−2ζ7−2ζ13+2ζ232ζ13−2ζ232−22−2ζ5−ζ7−ζ5+ζ7ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23ζ13−ζ23−ζ13+ζ23000000000000000000000000000
χ694-4-44400-4-44−222200−22−222222-2-2-22222-2−2323−232311-1-103−303−3−2ζ13+2ζ232ζ13−2ζ23−2ζ5+2ζ72ζ5−2ζ72−22−2ζ13−ζ23−ζ13+ζ23ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7ζ5−ζ7−ζ5+ζ7000000000000000000000000000
χ706666-366-3-3-366-3-3-3-3-3-300000000000000000000000000000000000000000002200000000000200-1-1-1-100
χ716666-366-3-3-366-3-3-3-3-3-30000000000000000000000000000000000000000000-2-200000000000-200111100
χ726666-366-3-3-3-6-6-3-3333300000000000000000000000000000000000000000002200000000000-200-1-11100
χ736666-366-3-3-3-6-6-3-333330000000000000000000000000000000000000000000-2-20000000000020011-1-100
χ746-66-6-36-63-33003-3−3i33i3−3i33i300000000000000000000000000000000000000000002i−2i00000000000000−ii3−300
χ756-66-6-36-63-33003-3−3i33i3−3i33i30000000000000000000000000000000000000000000−2i2i00000000000000i−i−3300
χ766-66-6-36-63-33003-33i3−3i33i3−3i300000000000000000000000000000000000000000002i−2i00000000000000−ii−3300
χ776-66-6-36-63-33003-33i3−3i33i3−3i30000000000000000000000000000000000000000000−2i2i00000000000000i−i3−300
χ7812121212-6-12-12-6-6-60066000000000000000000000000000000000000000000000000000000000000000000000
χ791212-12-12-600-66600003i6−3i6−3i63i600000000000000000000000000000000000000000000000000000000000000000
χ801212-12-12-600-6660000−3i63i63i6−3i600000000000000000000000000000000000000000000000000000000000000000
χ8112-1212-12-6-12126-6600-66000000000000000000000000000000000000000000000000000000000000000000000
χ8212-12-1212-60066-662−6200−32−32323200000000000000000000000000000000000000000000000000000000000000000
χ8312-12-1212-60066-6−6262003232−32−3200000000000000000000000000000000000000000000000000000000000000000

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