Finite Group Databasebeta

← Group #13156548

Character table — Group #13156548

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96
size11112222222222222244444444444444444488888888888888242424242424242424242424242424242424242424242424242424363636363636363636363636363636363636216
order12223334466666666633366666666612121212121236661212121212121212121224466666666121212121212121212121212121212124488881212121224242424242424244
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111-11111111111-1-111-1-11111-1-1-1-1-1-111-1-1-1-1-1-11111-1-1-1-1-1
χ3111111111111111111111111111111111111111111111111111-1111111111-1-111-1-111-1-1-1-11111-1-1-1-111-1-1-1-1-1-1-1-11111-1
χ4111111111111111111111111111111111111111111111111111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-11
χ511111111111111111111111111111111111111111111111111-111-1-1-1-1-1-1-1-1111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1
χ611111111111111111111111111111111111111111111111111-11-1-1-1-1-1-1-1-1-111-1-111-1-11111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111111
χ711111111111111111111111111111111111111111111111111-1-11-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-11111-1-111-1-1-1-1-1-11111-1-1-1-11
χ811111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111-1
χ92222222-2-2222222222222222222222-2-2-2-2-2-22222-2-2-2-2-2-2-2-2-2-20000000000000000000000000002-2000022-2-2000000000
χ102222222-2-2222222222222222222222-2-2-2-2-2-22222-2-2-2-2-2-2-2-2-2-2000000000000000000000000000-220000-2-222000000000
χ11222222-1222-122-12-1222-1-12-1-1-12-1-12-1222-12-1-1-1-1-122-1-1-1-1-1-1-1-120222-1-1-1-1-1-100-1-100220000-1-1-1-100002200000000-1-1-1-10
χ12222222-1222-122-12-1222-1-12-1-1-12-1-12-1222-12-1-1-1-1-122-1-1-1-1-1-1-1-120-222-1-1-1-1-1-1001100-2-2000011110000-2-20000000011110
χ13222222-1222-122-12-1222-1-12-1-1-12-1-12-1222-12-1-1-1-1-122-1-1-1-1-1-1-1-1-202-2-211111100-1-100220000-1-1-1-10000-2-20000000011110
χ14222222-1222-122-12-1222-1-12-1-1-12-1-12-1222-12-1-1-1-1-122-1-1-1-1-1-1-1-1-20-2-2-2111111001100-2-20000111100002200000000-1-1-1-10
χ1522222-1222-122-12-1222-12-1-12-1-1-12-1-1222-12-12-1-1-1-1-1-122-1-1-1-1-1-1220-1-122-1-1-1-1-1-1002200-1-1-1-100000022000000-1-1-1-100000
χ1622222-1222-122-12-1222-12-1-12-1-1-12-1-1222-12-12-1-1-1-1-1-122-1-1-1-1-1-12-20-1-122-1-1-1-11100-2-2001111000000-2-2000000111100000
χ1722222-1222-122-12-1222-12-1-12-1-1-12-1-1222-12-12-1-1-1-1-1-122-1-1-1-1-1-1-22011-2-21111-1-1002200-1-1-1-1000000-2-2000000111100000
χ1822222-1222-122-12-1222-12-1-12-1-1-12-1-1222-12-12-1-1-1-1-1-122-1-1-1-1-1-1-2-2011-2-211111100-2-200111100000022000000-1-1-1-100000
χ192222-1222222-12222-1-1-1-12-1-122-1-12-1-1-1-12222-1-1-1-1-1-1-1-122-1-1-1-1022000000002222-1-1-1-1-1-1-1-1-1-1-1-1220000-1-1-1-1000000000
χ202222-1222222-12222-1-1-1-12-1-122-1-12-1-1-1-12222-1-1-1-1-1-1-1-122-1-1-1-102-20000000022-2-2-1-111-1-1-1-11111-2-200001111000000000
χ212222-1222222-12222-1-1-1-12-1-122-1-12-1-1-1-12222-1-1-1-1-1-1-1-122-1-1-1-10-2200000000-2-22211-1-11111-1-1-1-1-2-200001111000000000
χ222222-1222222-12222-1-1-1-12-1-122-1-12-1-1-1-12222-1-1-1-1-1-1-1-122-1-1-1-10-2-200000000-2-2-2-2111111111111220000-1-1-1-1000000000
χ232222-122-2-222-12222-1-1-1-12-1-122-1-12-1-111-2-2-2-2-1-1-1-11111-2-21111000000000000000−i3i3−i3i3−i3−i3i3i3−i3−i3i3i32-20000-1-111000000000
χ242222-122-2-222-12222-1-1-1-12-1-122-1-12-1-111-2-2-2-2-1-1-1-11111-2-21111000000000000000−i3i3i3−i3−i3−i3i3i3i3i3−i3−i3-22000011-1-1000000000
χ252222-122-2-222-12222-1-1-1-12-1-122-1-12-1-111-2-2-2-2-1-1-1-11111-2-21111000000000000000i3−i3−i3i3i3i3−i3−i3−i3−i3i3i3-22000011-1-1000000000
χ262222-122-2-222-12222-1-1-1-12-1-122-1-12-1-111-2-2-2-2-1-1-1-11111-2-21111000000000000000i3−i3i3−i3i3i3−i3−i3i3i3−i3−i32-20000-1-111000000000
χ272-2-222222-2-2-2222-2-2-2-2222-2-2-2-2222-2-22-22-2-222-2-222-22-22-222-2-2000000000000000000000000000002i−2i0000002i2i−2i−2i00000
χ282-2-222222-2-2-2222-2-2-2-2222-2-2-2-2222-2-22-22-2-222-2-222-22-22-222-2-200000000000000000000000000000−2i2i000000−2i−2i2i2i00000
χ292-2-22222-22-2-2222-2-2-2-2222-2-2-2-2222-2-2-22-222-22-2-22-22-22-22-2-22200000000000000000000000000000002i−2i000000002i2i−2i−2i0
χ302-2-22222-22-2-2222-2-2-2-2222-2-2-2-2222-2-2-22-222-22-2-22-22-22-22-2-2220000000000000000000000000000000−2i2i00000000−2i−2i2i2i0
χ312-2-2222-1-22-2122-1-21-2-22-1-1-21112-1-1-21-22-2-121-111-1-221-11-111-1-100000−i3i3−i3−i3i3i3003−3000000003−33−300002i−2i00000000−i−iii0
χ322-2-2222-1-22-2122-1-21-2-22-1-1-21112-1-1-21-22-2-121-111-1-221-11-111-1-100000−i3i3−i3−i3i3i300−3300000000−33−330000−2i2i00000000ii−i−i0
χ332-2-2222-1-22-2122-1-21-2-22-1-1-21112-1-1-21-22-2-121-111-1-221-11-111-1-100000i3−i3i3i3−i3−i3003−3000000003−33−30000−2i2i00000000ii−i−i0
χ342-2-2222-1-22-2122-1-21-2-22-1-1-21112-1-1-21-22-2-121-111-1-221-11-111-1-100000i3−i3i3i3−i3−i300−3300000000−33−3300002i−2i00000000−i−iii0
χ352-2-222-122-21-22-121-2-2-2-12-11-211-12-11-22-2-1-212-111-1-112-2-11-1-111000−i3i300−i3i3−i3i33−30000003−33−30000002i−2i000000−i−iii00000
χ362-2-222-122-21-22-121-2-2-2-12-11-211-12-11-22-2-1-212-111-1-112-2-11-1-111000−i3i300−i3i3−i3i3−33000000−33−33000000−2i2i000000ii−i−i00000
χ372-2-222-122-21-22-121-2-2-2-12-11-211-12-11-22-2-1-212-111-1-112-2-11-1-111000i3−i300i3−i3i3−i33−30000003−33−3000000−2i2i000000ii−i−i00000
χ382-2-222-122-21-22-121-2-2-2-12-11-211-12-11-22-2-1-212-111-1-112-2-11-1-111000i3−i300i3−i3i3−i3−33000000−33−330000002i−2i000000−i−iii00000
χ39444444-2-4-44-244-24-2444-2-24-2-2-24-2-24-2-4-4-42-42-2-2-2-2-4-4222222220000000000000000000000000000000000000000000000
χ4044444-24-4-4-244-24-2444-24-2-24-2-2-24-2-24-4-42-42-4-2-2-2-222-4-42222220000000000000000000000000000000000000000000000
χ4144444-2-244-2-24-2-2-2-244-2-21-2-211-2-21-2-244-2-2-2-21111-2-2-2-2111111400-2-2-2-2111100000000000000000000000000000000000
χ4244444-2-244-2-24-2-2-2-244-2-21-2-211-2-21-2-244-2-2-2-21111-2-2-2-2111111-4002222-1-1-1-100000000000000000000000000000000000
χ4344444-2-2-4-4-2-24-2-2-2-244-2-21-2-211-2-21-2-2-4-4222211112222-1-1-1-1-1-100000003-3-3300000000000000000000000000000000000
χ4444444-2-2-4-4-2-24-2-2-2-244-2-21-2-211-2-21-2-2-4-4222211112222-1-1-1-1-1-10000000-333-300000000000000000000000000000000000
χ454444-24-2444-2-24-24-2-2-2-21-2-21-2-2-21-2-21-2-24-24-21111-2-211-2-211110040000000000-2-200-2-2000011110000000000000000000
χ464444-24-2444-2-24-24-2-2-2-21-2-21-2-2-21-2-21-2-24-24-21111-2-211-2-2111100-400000000002200220000-1-1-1-10000000000000000000
χ474444-24-2-4-44-2-24-24-2-2-2-21-2-21-2-2-21-2-2122-42-42111122-1-122-1-1-1-100000000000000000−2i32i30000i3i3−i3−i30000000000000000000
χ484444-24-2-4-44-2-24-24-2-2-2-21-2-21-2-2-21-2-2122-42-42111122-1-122-1-1-1-1000000000000000002i3−2i30000−i3−i3i3i30000000000000000000
χ494444-2-2444-24-2-24-24-2-21-2-21-2-2-21-2-21-2-2-2-24-24111111-2-2-2-2111104000000000-2-200-2-200111100000000000000000000000
χ504444-2-2444-24-2-24-24-2-21-2-21-2-2-21-2-21-2-2-2-24-24111111-2-2-2-211110-400000000022002200-1-1-1-100000000000000000000000
χ514444-2-24-4-4-24-2-24-24-2-21-2-21-2-2-21-2-21-2222-42-41111-1-12222-1-1-1-1000000000000000−2i32i300i3i3−i3−i300000000000000000000000
χ524444-2-24-4-4-24-2-24-24-2-21-2-21-2-2-21-2-21-2222-42-41111-1-12222-1-1-1-10000000000000002i3−2i300−i3−i3i3i300000000000000000000000
χ5344-4-44440044-4-4-4-4-44-4444444-4-4-4-4-4-400000044-4-400000000000000000000000000000000000000000000000000000000
χ5444-4-444-2004-2-4-42-424-44-2-24-2-22-422-42000000-2-2220000000000000000000000000000000000000000000000000006−66−60
χ5544-4-444-2004-2-4-42-424-44-2-24-2-22-422-42000000-2-222000000000000000000000000000000000000000000000000000−66−660
χ5644-4-44-2400-24-42-42-44-4-24-2-24-222-422-4000000-2-222000000000000000000000000000000000000000000000006−66−600000
χ5744-4-44-2400-24-42-42-44-4-24-2-24-222-422-4000000-2-22200000000000000000000000000000000000000000000000−66−6600000
χ5844-4-4-24400442-4-4-4-4-22-2-24-2-24-422-422000000-2-2220000000000000000000000000000000000000000000−2i32i300000000000
χ5944-4-4-24400442-4-4-4-4-22-2-24-2-24-422-422000000-2-22200000000000000000000000000000000000000000002i3−2i300000000000
χ604-44-444400-4-4-4-4-444-44444-4-4-44-4-4-4440000004-44-400000000000000000000000000000000000000000000000000000000
χ614-44-444-200-42-4-424-2-444-2-2-422-2-4224-2000000-22-22000000000000000000000000000000000000000000000000000i6−i6−i6i60
χ624-44-444-200-42-4-424-2-444-2-2-422-2-4224-2000000-22-22000000000000000000000000000000000000000000000000000−i6i6i6−i60
χ634-44-44-24002-4-42-4-24-44-24-22-42-22-42-24000000-22-2200000000000000000000000000000000000000000000000i6−i6−i6i600000
χ644-44-44-24002-4-42-4-24-44-24-22-42-22-42-24000000-22-2200000000000000000000000000000000000000000000000−i6i6i6−i600000
χ654-44-4-24400-4-42-4-4442-2-2-2422-4422-4-2-2000000-22-22000000000000000000000000000000000000000000000−2i32i3000000000
χ664-44-4-24400-4-42-4-4442-2-2-2422-4422-4-2-2000000-22-220000000000000000000000000000000000000000000002i3−2i3000000000
χ674-4-4444-24-4-4244-2-42-4-44-2-2-42224-2-2-424-442-4-2-222-24-4-22-22-2-2220000000000000000000000000000000000000000000000
χ684-4-444-24-442-44-242-4-4-4-24-22-422-24-22-4-4424-2-4-222-22-2-442-222-2-20000000000000000000000000000000000000000000000
χ694-4-444-2-24-4224-2-222-4-4-2-2122-1-1-2-21224-4-222-21-1-11-22-221-111-1-1000−2i32i300i3−i3i3−i300000000000000000000000000000000000
χ704-4-444-2-24-4224-2-222-4-4-2-2122-1-1-2-21224-4-222-21-1-11-22-221-111-1-10002i3−2i300−i3i3−i3i300000000000000000000000000000000000
χ714-4-444-2-2-44224-2-222-4-4-2-2122-1-1-2-2122-442-2-221-1-112-22-2-11-1-11100000−2i32i3i3i3−i3−i300000000000000000000000000000000000
χ724-4-444-2-2-44224-2-222-4-4-2-2122-1-1-2-2122-442-2-221-1-112-22-2-11-1-111000002i3−2i3−i3−i3i3i300000000000000000000000000000000000
χ734-4-44-2444-4-4-4-244-4-422-2-2422-4-4-2-2422-224-4-44-222-2-22-224-4-2-2220000000000000000000000000000000000000000000000
χ744-4-44-244-44-4-4-244-4-422-2-2422-4-4-2-24222-2-444-4-222-22-22-2-4422-2-20000000000000000000000000000000000000000000000
χ754-4-44-24-24-4-42-24-2-4222-21-22-122-21-22-1-2242-4-21-1-11-221-1-2211-1-1000000000000000000000003i−3i−3i3i0000000000000000000
χ764-4-44-24-24-4-42-24-2-4222-21-22-122-21-22-1-2242-4-21-1-11-221-1-2211-1-100000000000000000000000−3i3i3i−3i0000000000000000000
χ774-4-44-24-2-44-42-24-2-4222-21-22-122-21-22-12-2-4-2421-1-112-2-112-2-1-111000000000000023−2300000000−33−330000000000000000000
χ784-4-44-24-2-44-42-24-2-4222-21-22-122-21-22-12-2-4-2421-1-112-2-112-2-1-1110000000000000−2323000000003−33−30000000000000000000
χ794-4-44-2-244-42-4-2-242-4221-2-2-12221-2-2-12-22-2-4241-1-111-1-22-2211-1-10000000000023−23000000−33−3300000000000000000000000
χ804-4-44-2-244-42-4-2-242-4221-2-2-12221-2-2-12-22-2-4241-1-111-1-22-2211-1-100000000000−23230000003−33−300000000000000000000000
χ814-4-44-2-24-442-4-2-242-4221-2-2-12221-2-2-122-224-2-41-1-11-112-22-2-1-11100000000000000000003i−3i−3i3i00000000000000000000000
χ824-4-44-2-24-442-4-2-242-4221-2-2-12221-2-2-122-224-2-41-1-11-112-22-2-1-1110000000000000000000−3i3i3i−3i00000000000000000000000
χ838888-4-4-488-4-4-4-4-4-4-4-4-4222222222222-4-4-4-4-4-4-1-1-1-1222222-1-1-1-10000000000000000000000000000000000000000000000
χ848888-4-4-4-8-8-4-4-4-4-4-4-4-4-4222222222222444444-1-1-1-1-2-2-2-2-2-211110000000000000000000000000000000000000000000000
χ8588-8-88-4-400-4-4-844448-8-4-42-4-42-244-24400000022-2-200000000000000000000000000000000000000000000000000000000
χ8688-8-8-48-4008-44-84-84-44-42-4-42-444-244-200000022-2-200000000000000000000000000000000000000000000000000000000
χ8788-8-8-4-4800-4844-84-8-442-4-42-4-44-244-2400000022-2-200000000000000000000000000000000000000000000000000000000
χ8888-8-8-4-4-400-4-444444-44222222-2-2-2-2-2-2000000-1-11100000033−3333−330000000000000000000000000000000000000000000000
χ8988-8-8-4-4-400-4-444444-44222222-2-2-2-2-2-2000000-1-111000000−3333−33330000000000000000000000000000000000000000000000
χ908-88-88-4-40044-844-4-4-88-4-4244-2244-2-4-40000002-22-200000000000000000000000000000000000000000000000000000000
χ918-88-8-48-400-844-848-44-4-42-44-24-44-24-420000002-22-200000000000000000000000000000000000000000000000000000000
χ928-88-8-4-48004-844-8-484-42-4-4-244-4-2442-40000002-22-200000000000000000000000000000000000000000000000000000000
χ938-88-8-4-4-40044444-4-44-4222-2-2-22-2-2-222000000-11-1100000033−33−33330000000000000000000000000000000000000000000000
χ948-88-8-4-4-40044444-4-44-4222-2-2-22-2-2-222000000-11-11000000−333333−330000000000000000000000000000000000000000000000
χ958-8-88-4-4-48-844-4-4-44444222-2-2-2-2222-2-2-44-444-4-111-12-22-22-2-1-1110000000000000000000000000000000000000000000000
χ968-8-88-4-4-4-8844-4-4-44444222-2-2-2-2222-2-24-44-4-44-111-1-22-22-2211-1-10000000000000000000000000000000000000000000000

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