Finite Group Databasebeta

← Group #13156454

Character table — Group #13156454

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99
size111122222222222222444444444444444444888888888888881212181824242424242424242424242424242424242424242424242424243636363636363636363636363636363636108108
order12223334466666666633366666666612121212121236661212121212121212121244224412121212121212121212121212121212121212121212121246688881212242424242424242444
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111-1-1-1-111-1-1-1-1-1-1-1-111
χ31111111111111111111111111111111111111111111111111111-1-11-111111111-1-1-1-111111111-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-1-1-1
χ41111111111111111111111111111111111111111111111111111-1-1-111111-1-1-1-111111111-1-1-1-11111-1-1-1-1-111-1-1-1-1-1-11111-1-1
χ511111111111111111111111111111111111111111111111111-1-11111-1-1-1-111111111-1-1-1-111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1
χ611111111111111111111111111111111111111111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111111-1-1
χ711111111111111111111111111111111111111111111111111-1-1-1-11-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1111111
χ811111111111111111111111111111111111111111111111111-1-1-1-1-11-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-111-1-1-1-11111-1-1-1-111
χ92222222-2-2222222222222222222222-2-2-2-2-2-22222-2-2-2-2-2-2-2-2-2-2002200000000000000000000000000-2220000-2-20000000000
χ102222222-2-2222222222222222222222-2-2-2-2-2-22222-2-2-2-2-2-2-2-2-2-200-2-2000000000000000000000000002-2-20000220000000000
χ11222222-1222-12222-12-12-1-12-1-1-12-12-1-122-1-122-1-1-1-122-1-1-1-1-1-1-1-1002222000022-1-122-1-10000-1-1-1-1-1-1-1-12-1-10000-1-10000000000
χ12222222-1222-12222-12-12-1-12-1-1-12-12-1-122-1-122-1-1-1-122-1-1-1-1-1-1-1-10022-2-20000-2-211-2-2110000111111112-1-10000-1-10000000000
χ13222222-1222-12222-12-12-1-12-1-1-12-12-1-122-1-122-1-1-1-122-1-1-1-1-1-1-1-100-2-22-2000022-1-1-2-2110000-1-1-1-11111-2110000110000000000
χ14222222-1222-12222-12-12-1-12-1-1-12-12-1-122-1-122-1-1-1-122-1-1-1-1-1-1-1-100-2-2-220000-2-21122-1-100001111-1-1-1-1-2110000110000000000
χ15222222-1-2-22-12222-12-12-1-12-1-1-12-12-1-1-2-211-2-2-1-1-1-1-2-211111111002200000000−i3i300−i3i30000−i3−i3i3i3−i3−i3i3i3-2-1-10000110000000000
χ16222222-1-2-22-12222-12-12-1-12-1-1-12-12-1-1-2-211-2-2-1-1-1-1-2-211111111002200000000i3−i300i3−i30000i3i3−i3−i3i3i3−i3−i3-2-1-10000110000000000
χ17222222-1-2-22-12222-12-12-1-12-1-1-12-12-1-1-2-211-2-2-1-1-1-1-2-21111111100-2-200000000−i3i300i3−i30000−i3−i3i3i3i3i3−i3−i32110000-1-10000000000
χ18222222-1-2-22-12222-12-12-1-12-1-1-12-12-1-1-2-211-2-2-1-1-1-1-2-21111111100-2-200000000i3−i300−i3i30000i3i3−i3−i3−i3−i3i3i32110000-1-10000000000
χ1922222-122222-12-1-1222-12-1-122-1-1-1-1-12-1222-12-1-1-1-1-1-1-1-122-1-1-1-122002022-1-1-1-1220000-1-1-1-1-1-1-1-10000000220000-1-1-1-1000000
χ2022222-122222-12-1-1222-12-1-122-1-1-1-1-12-1222-12-1-1-1-1-1-1-1-122-1-1-1-12200-2022-1-111-2-20000-1-1-1-111110000000-2-200001111000000
χ2122222-122222-12-1-1222-12-1-122-1-1-1-1-12-1222-12-1-1-1-1-1-1-1-122-1-1-1-1-2-20020-2-211-1-12200001111-1-1-1-10000000-2-200001111000000
χ2222222-122222-12-1-1222-12-1-122-1-1-1-1-12-1222-12-1-1-1-1-1-1-1-122-1-1-1-1-2-200-20-2-21111-2-20000111111110000000220000-1-1-1-1000000
χ232222-12222-122-1222-12-1-12-1-1-12-12-12-12-1222-1-1-1-1-1-1-122-1-1-1-1-1-1220002-1-1220000-1-122-1-1-1-10000-1-1-1-10000022000000-1-1-1-100
χ242222-12222-122-1222-12-1-12-1-1-12-12-12-12-1222-1-1-1-1-1-1-122-1-1-1-1-1-122000-2-1-122000011-2-2-1-1-1-10000111100000-2-2000000111100
χ252222-12222-122-1222-12-1-12-1-1-12-12-12-12-1222-1-1-1-1-1-1-122-1-1-1-1-1-1-2-2000211-2-20000-1-12211110000-1-1-1-100000-2-2000000111100
χ262222-12222-122-1222-12-1-12-1-1-12-12-12-12-1222-1-1-1-1-1-1-122-1-1-1-1-1-1-2-2000-211-2-2000011-2-21111000011110000022000000-1-1-1-100
χ272-22-22222-2-2-22-2-2-2-222222-2-2-2-222-2-222-22-2-222-2-222-22-22-222-2-2000000000000000000000000000000000000000000000002i−2i
χ282-22-22222-2-2-22-2-2-2-222222-2-2-2-222-2-222-22-2-222-2-222-22-22-222-2-200000000000000000000000000000000000000000000000−2i2i
χ292-22-2222-22-2-22-2-2-2-222222-2-2-2-222-2-22-22-222-22-2-22-22-22-22-2-2222i−2i00002i−2i2i−2i000000002i2i−2i−2i000000000000000000000000000
χ302-22-2222-22-2-22-2-2-2-222222-2-2-2-222-2-22-22-222-22-2-22-22-22-22-2-222−2i2i0000−2i2i−2i2i00000000−2i−2i2i2i000000000000000000000000000
χ312-22-22-12-22-2-2-1-211-222-12-11-2-21-1-111212-22-1-2-111-11-11-1-2211-1-12i−2i00002i−2i−ii3−3000000−i−iii3−33−30000000000000−i3−i3i3i3000000
χ322-22-22-12-22-2-2-1-211-222-12-11-2-21-1-111212-22-1-2-111-11-11-1-2211-1-12i−2i00002i−2i−ii−33000000−i−iii−33−330000000000000i3i3−i3−i3000000
χ332-22-22-12-22-2-2-1-211-222-12-11-2-21-1-111212-22-1-2-111-11-11-1-2211-1-1−2i2i0000−2i2ii−i3−3000000ii−i−i3−33−30000000000000i3i3−i3−i3000000
χ342-22-22-12-22-2-2-1-211-222-12-11-2-21-1-111212-22-1-2-111-11-11-1-2211-1-1−2i2i0000−2i2ii−i−33000000ii−i−i−33−330000000000000−i3−i3i3i3000000
χ352-22-2-122-221-221-2-2-2-12-1-12111-2-121-2-1-2-1-2221-111-11-1-221-111-1-12i−2i0000−ii2i−2i0000−i3i300−i−iii0000−i3i3−i3i3000000000000033−3−300
χ362-22-2-122-221-221-2-2-2-12-1-12111-2-121-2-1-2-1-2221-111-11-1-221-111-1-12i−2i0000−ii2i−2i0000i3−i300−i−iii0000i3−i3i3−i30000000000000−3−33300
χ372-22-2-122-221-221-2-2-2-12-1-12111-2-121-2-1-2-1-2221-111-11-1-221-111-1-1−2i2i0000i−i−2i2i0000−i3i300ii−i−i0000−i3i3−i3i30000000000000−3−33300
χ382-22-2-122-221-221-2-2-2-12-1-12111-2-121-2-1-2-1-2221-111-11-1-221-111-1-1−2i2i0000i−i−2i2i0000i3−i300ii−i−i0000i3−i3i3−i3000000000000033−3−300
χ392-2-2222200-22-222-2-2-2-2222-22-22-2-22-2-200000022-2-20000000000002-20000000000000000000000000002-2−i2i2−i2i200−i2i2−i2i2−i2i2−i2i200
χ402-2-2222200-22-222-2-2-2-2222-22-22-2-22-2-200000022-2-20000000000002-20000000000000000000000000002-2i2−i2i2−i200i2−i2i2−i2i2−i2i2−i200
χ412-2-2222200-22-222-2-2-2-2222-22-22-2-22-2-200000022-2-2000000000000-22000000000000000000000000000-22−i2i2i2−i200−i2i2−i2i2i2−i2i2−i200
χ422-2-2222200-22-222-2-2-2-2222-22-22-2-22-2-200000022-2-2000000000000-22000000000000000000000000000-22i2−i2−i2i200i2−i2i2−i2−i2i2−i2i200
χ4344444-24-4-444-24-2-2444-24-2-244-2-2-2-2-242-4-4-42-4-2-2-2-22222-4-422220000000000000000000000000000000000000000000000000
χ4444444-2-2444-2-24-2-2-24-2-2-21-2-2-21-21-21-2-24-2-2-241111-2-211-2-211110000400000-2-2-2-200000000111100000000000000000000000
χ4544444-2-2444-2-24-2-2-24-2-2-21-2-2-21-21-21-2-24-2-2-241111-2-211-2-211110000-400000222200000000-1-1-1-100000000000000000000000
χ4644444-2-2-4-44-2-24-2-2-24-2-2-21-2-2-21-21-21-22-4222-4111122-1-122-1-1-1-1000000000000−2i32i300000000i3i3−i3−i300000000000000000000000
χ4744444-2-2-4-44-2-24-2-2-24-2-2-21-2-2-21-21-21-22-4222-4111122-1-122-1-1-1-10000000000002i3−2i300000000−i3−i3i3i300000000000000000000000
χ484444-244-4-4-244-2444-24-2-24-2-2-24-24-24-2-42-4-4-42-2-2-2-222-4-42222220000000000000000000000000000000000000000000000000
χ494444-24-244-2-24-244-2-2-2-21-2-211-2-2-2-2-214-2-2-24-21111-2-2-2-211111100000400000000-2-2-2-20000000011110000000000000000000
χ504444-24-244-2-24-244-2-2-2-21-2-211-2-2-2-2-214-2-2-24-21111-2-2-2-211111100000-400000000222200000000-1-1-1-10000000000000000000
χ514444-24-2-4-4-2-24-244-2-2-2-21-2-211-2-2-2-2-21-4222-4211112222-1-1-1-1-1-10000000000000000−2i32i300000000i3i3−i3−i30000000000000000000
χ524444-24-2-4-4-2-24-244-2-2-2-21-2-211-2-2-2-2-21-4222-4211112222-1-1-1-1-1-100000000000000002i3−2i300000000−i3−i3i3i30000000000000000000
χ534444-2-2444-24-2-2-2-24-241-2-21-2-2-21-21-2-2-2-244-2-2111111-2-2-2-21111440000-2-2-2-2000000001111000000000000000000000000000
χ544444-2-2444-24-2-2-2-24-241-2-21-2-2-21-21-2-2-2-244-2-2111111-2-2-2-21111-4-40000222200000000-1-1-1-1000000000000000000000000000
χ554444-2-24-4-4-24-2-2-2-24-241-2-21-2-2-21-21-2-222-4-4221111-1-12222-1-1-1-10000000000000000003-33-3000000000000000000000000000
χ564444-2-24-4-4-24-2-2-2-24-241-2-21-2-2-21-21-2-222-4-4221111-1-12222-1-1-1-1000000000000000000-33-33000000000000000000000000000
χ5744-4-4444004-4-4-4-444-4-44444-44-4-4-4-44-40000004-44-400000000000000000000000000000000000000000000000000000000000
χ5844-4-444-20042-4-4-44-2-424-2-242-22-42-4-22000000-22-220000000000000000000000000000000000000000000000023−230000000000
χ5944-4-444-20042-4-4-44-2-424-2-242-22-42-4-22000000-22-2200000000000000000000000000000000000000000000000−23230000000000
χ6044-4-44-24004-42-42-24-4-4-24-2-2-442222-2-4000000-22-2200000000000000000000000000000000000000000000000006−6−66000000
χ6144-4-44-24004-42-42-24-4-4-24-2-2-442222-2-4000000-22-220000000000000000000000000000000000000000000000000−666−6000000
χ6244-4-4-24400-2-4-42-4442-4-2-24-22-2-42-4242000000-22-2200000000000000000000000000000000000000000000000000000i6−i6−i6i600
χ6344-4-4-24400-2-4-42-4442-4-2-24-22-2-42-4242000000-22-2200000000000000000000000000000000000000000000000000000−i6i6i6−i600
χ644-44-444-24-4-424-4-4-424-24-2-2-42224-2-42-24-4-22-44-222-24-4-22-22-2-2220000000000000000000000000000000000000000000000000
χ654-44-444-2-44-424-4-4-424-24-2-2-42224-2-42-2-442-24-4-222-2-442-22-222-2-20000000000000000000000000000000000000000000000000
χ664-44-44-244-4-4-4-2-422-444-24-22-4-42-2-2224-2-44-424-222-2-22-224-4-2-2220000000000000000000000000000000000000000000000000
χ674-44-44-2-24-4-42-2-42224-2-2-21222-1-212-1-2-2-4-22241-1-11-221-1-2211-1-100000000000000000000003i−3i−3i3i00000000000000000000000
χ684-44-44-2-24-4-42-2-42224-2-2-21222-1-212-1-2-2-4-22241-1-11-221-1-2211-1-10000000000000000000000−3i3i3i−3i00000000000000000000000
χ694-44-44-2-2-44-42-2-42224-2-2-21222-1-212-1-2242-2-2-41-1-112-2-112-2-1-111000000000023−230000000000−33−3300000000000000000000000
χ704-44-44-2-2-44-42-2-42224-2-2-21222-1-212-1-2242-2-2-41-1-112-2-112-2-1-1110000000000−232300000000003−33−300000000000000000000000
χ714-44-4-2444-42-442-4-4-4-24-2-24222-4-242-4-2424-4-4-2-222-2-224-4-22-2-2220000000000000000000000000000000000000000000000000
χ724-44-4-24-24-42242-4-42-2-2-21-22-1-12-2-222142-22-4-21-1-11-22-221-111-1-1000000000000000000000000003-3-330000000000000000000
χ734-44-4-24-24-42242-4-42-2-2-21-22-1-12-2-222142-22-4-21-1-11-22-221-111-1-100000000000000000000000000-333-30000000000000000000
χ744-44-4-24-2-442242-4-42-2-2-21-22-1-12-2-2221-4-22-2421-1-112-22-2-11-1-11100000000000000−2i32i30000000000i3−i3i3−i30000000000000000000
χ754-44-4-24-2-442242-4-42-2-2-21-22-1-12-2-2221-4-22-2421-1-112-22-2-11-1-111000000000000002i3−2i30000000000−i3i3−i3i30000000000000000000
χ764-44-4-2-244-42-4-2222-4-241-2-2-12221-2-12-2-224-42-21-1-111-1-22-2211-1-10000000000000000003i−3i−3i3i000000000000000000000000000
χ774-44-4-2-244-42-4-2222-4-241-2-2-12221-2-12-2-224-42-21-1-111-1-22-2211-1-1000000000000000000−3i3i3i−3i000000000000000000000000000
χ784-44-4-2-24-442-4-2222-4-241-2-2-12221-2-12-22-2-44-221-1-11-112-22-2-1-1114i−4i0000−2i2i−2i2i00000000ii−i−i000000000000000000000000000
χ794-44-4-2-24-442-4-2222-4-241-2-2-12221-2-12-22-2-44-221-1-11-112-22-2-1-111−4i4i00002i−2i2i−2i00000000−i−iii000000000000000000000000000
χ804-4-4444-200-4-2-444-42-424-2-2-4-22-2-42422000000-2-2220000000000004-4000000000000000000000000000-220000000000000000
χ814-4-4444-200-4-2-444-42-424-2-2-4-22-2-42422000000-2-222000000000000-440000000000000000000000000002-20000000000000000
χ824-4-444-2400-4424-22-4-4-4-24-224-4-222-22-4000000-2-2220000000000000000000000000000000000000000000−2i22i20000i2−i2i2−i2000000
χ834-4-444-2400-4424-22-4-4-4-24-224-4-222-22-4000000-2-22200000000000000000000000000000000000000000002i2−2i20000−i2i2−i2i2000000
χ844-4-44-2440024-4-24-4-42-4-2-242-2242-4-2-42000000-2-222000000000000000000000000000000000000000000000−2i22i2000000i2−i2i2−i200
χ854-4-44-2440024-4-24-4-42-4-2-242-2242-4-2-42000000-2-2220000000000000000000000000000000000000000000002i2−2i2000000−i2i2−i2i200
χ868888-4-4-488-4-4-4-4-4-4-4-4-4222222222222-4-4-4-4-4-4-1-1-1-1222222-1-1-1-10000000000000000000000000000000000000000000000000
χ878888-4-4-4-8-8-4-4-4-4-4-4-4-4-4222222222222444444-1-1-1-1-2-2-2-2-2-211110000000000000000000000000000000000000000000000000
χ8888-8-88-4-400844-84-4-4-84-4-42-44-4-24-24240000002-22-200000000000000000000000000000000000000000000000000000000000
χ8988-8-8-48-400-44-84-88-444-42-4-4-224444-4-20000002-22-200000000000000000000000000000000000000000000000000000000000
χ9088-8-8-4-4800-4-8444-484-82-4-424-44-24-2-440000002-22-200000000000000000000000000000000000000000000000000000000000
χ9188-8-8-4-4-400-44444-4-4442222-22-2-2-2-22-2000000-11-1100000033−3333−330000000000000000000000000000000000000000000000000
χ9288-8-8-4-4-400-44444-4-4442222-22-2-2-2-22-2000000-11-11000000−3333−33330000000000000000000000000000000000000000000000000
χ938-88-8-4-4-48-844-44444-4-4222-2-2-2-222-2-22-44-444-4-111-12-22-22-2-1-1110000000000000000000000000000000000000000000000000
χ948-88-8-4-4-4-8844-44444-4-4222-2-2-2-222-2-224-44-4-44-111-1-22-22-2211-1-10000000000000000000000000000000000000000000000000
χ958-8-888-4-400-8-448-444-84-4-424-4424-2-4-2400000022-2-200000000000000000000000000000000000000000000000000000000000
χ968-8-88-48-4004-4-8-48-8444-42-442-2-444-44-200000022-2-200000000000000000000000000000000000000000000000000000000000
χ978-8-88-4-4800484-4-44-84-82-4-4-2-44-4-2424400000022-2-200000000000000000000000000000000000000000000000000000000000
χ988-8-88-4-4-4004-44-4-44444222-22-22-2-22-2-2000000-1-11100000033−33−33330000000000000000000000000000000000000000000000000
χ998-8-88-4-4-4004-44-4-44444222-22-22-2-22-2-2000000-1-111000000−333333−330000000000000000000000000000000000000000000000000

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