Finite Group Databasebeta

← Group #13156431

Character table — Group #13156431

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99
size111122222222222222444444444444444444888888888888881212181824242424242424242424242424242424242424242424242424243636363636363636363636363636363636108108
order122233344666666666333666666666121212121212366612121212121212121212444424666666661212121212121212121212121212121226688881212242424242424242444
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1111-1-1-1-111-1-1-1-1-1-1-1-111
χ31111111111111111111111111111111111111111111111111111-1-11-1111111111111-1-1-1-11111-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-1-1-1
χ41111111111111111111111111111111111111111111111111111-1-1-11-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-111-1-1-1-1-1-11111-1-1
χ511111111111111111111111111111111111111111111111111-1-1111111111111-1-1-1-11111-1-1-1-11111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1
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
χ711111111111111111111111111111111111111111111111111-1-1-1-11-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1111111
χ811111111111111111111111111111111111111111111111111-1-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-111-1-1-1-11111-1-1-1-111
χ92222222-2-2222222222222222222222-2-2-2-2-2-22222-2-2-2-2-2-2-2-2-2-2002200000000000000000000000000-2-2-20000220000000000
χ102222222-2-2222222222222222222222-2-2-2-2-2-22222-2-2-2-2-2-2-2-2-2-200-2-2000000000000000000000000002220000-2-20000000000
χ11222222-1222-122222-1-12-1-12-1-1-12-1-12-122-1-122-1-1-1-122-1-1-1-1-1-1-1-100222222-1-1-1-1-1-1000022-1-10000-1-1-1-12-1-10000-1-10000000000
χ12222222-1222-122222-1-12-1-12-1-1-12-1-12-122-1-122-1-1-1-122-1-1-1-1-1-1-1-10022-2-2-2-21111110000-2-211000011112-1-10000-1-10000000000
χ13222222-1222-122222-1-12-1-12-1-1-12-1-12-122-1-122-1-1-1-122-1-1-1-1-1-1-1-100-2-22-222-1-1-1-1-1-10000-2-21100001111-2110000110000000000
χ14222222-1222-122222-1-12-1-12-1-1-12-1-12-122-1-122-1-1-1-122-1-1-1-1-1-1-1-100-2-2-22-2-2111111000022-1-10000-1-1-1-1-2110000110000000000
χ15222222-1-2-22-122222-1-12-1-12-1-1-12-1-12-1-2-211-2-2-1-1-1-1-2-21111111100220000−i3i3−i3−i3i3i3000000−i3i30000−i3−i3i3i3-2110000-1-10000000000
χ16222222-1-2-22-122222-1-12-1-12-1-1-12-1-12-1-2-211-2-2-1-1-1-1-2-21111111100220000i3−i3i3i3−i3−i3000000i3−i30000i3i3−i3−i3-2110000-1-10000000000
χ17222222-1-2-22-122222-1-12-1-12-1-1-12-1-12-1-2-211-2-2-1-1-1-1-2-21111111100-2-20000−i3i3−i3−i3i3i3000000i3−i30000i3i3−i3−i32-1-10000110000000000
χ18222222-1-2-22-122222-1-12-1-12-1-1-12-1-12-1-2-211-2-2-1-1-1-1-2-21111111100-2-20000i3−i3i3i3−i3−i3000000−i3i30000−i3−i3i3i32-1-10000110000000000
χ1922222-1222-122-122-122-12-1-12-1-1-12-1-122-1222-1-1-1-1-1-1-122-1-1-1-1-1-1220020-1-122-1-1-1-122-1-10000-1-1-1-10000000220000-1-1-1-1000000
χ2022222-1222-122-122-122-12-1-12-1-1-12-1-122-1222-1-1-1-1-1-1-122-1-1-1-1-1-12200-2011-2-2111122-1-10000-1-1-1-10000000-2-200001111000000
χ2122222-1222-122-122-122-12-1-12-1-1-12-1-122-1222-1-1-1-1-1-1-122-1-1-1-1-1-1-2-20020-1-122-1-1-1-1-2-211000011110000000-2-200001111000000
χ2222222-1222-122-122-122-12-1-12-1-1-12-1-122-1222-1-1-1-1-1-1-122-1-1-1-1-1-1-2-200-2011-2-21111-2-211000011110000000220000-1-1-1-1000000
χ232222-1222222-12-1-1222-1-12-1-122-1-12-1-1-1222-12-1-1-1-1-1-1-1-122-1-1-1-122000200000000-1-122-1-122-1-1-1-1-1-1-1-10000022000000-1-1-1-100
χ242222-1222222-12-1-1222-1-12-1-122-1-12-1-1-1222-12-1-1-1-1-1-1-1-122-1-1-1-122000-200000000-1-12211-2-2-1-1-1-1111100000-2-2000000111100
χ252222-1222222-12-1-1222-1-12-1-122-1-12-1-1-1222-12-1-1-1-1-1-1-1-122-1-1-1-1-2-200020000000011-2-2-1-1221111-1-1-1-100000-2-2000000111100
χ262222-1222222-12-1-1222-1-12-1-122-1-12-1-1-1222-12-1-1-1-1-1-1-1-122-1-1-1-1-2-2000-20000000011-2-211-2-2111111110000022000000-1-1-1-100
χ2722-2-222200-22-2-22-22-2-2222-222-2-2-2-22-200000022-2-20000000000002i−2i000000000000000000000000000002−2−i2i22i−2i22−2−2−i2−i2i2i200
χ2822-2-222200-22-2-22-22-2-2222-222-2-2-2-22-200000022-2-20000000000002i−2i00000000000000000000000000000−22i2−i22i−2i−2−222i2i2−i2−i200
χ2922-2-222200-22-2-22-22-2-2222-222-2-2-2-22-200000022-2-2000000000000−2i2i000000000000000000000000000002−2i2−i2−2i2i22−2−2i2i2−i2−i200
χ3022-2-222200-22-2-22-22-2-2222-222-2-2-2-22-200000022-2-2000000000000−2i2i00000000000000000000000000000−22−i2i2−2i2i−2−222−i2−i2i2i200
χ312-22-22222-2-2-222-2-2-2-22222-2-2-2-2222-2-22-22-2-222-2-222-22-22-222-2-2000000000000000000000000000000000000000000000002i−2i
χ322-22-22222-2-2-222-2-2-2-22222-2-2-2-2222-2-22-22-2-222-2-222-22-22-222-2-200000000000000000000000000000000000000000000000−2i2i
χ332-22-2222-22-2-222-2-2-2-22222-2-2-2-2222-2-2-22-222-22-2-22-22-22-22-2-2222i−2i0000000000002i−2i2i−2i00002i2i−2i−2i00000000000000000000000
χ342-22-2222-22-2-222-2-2-2-22222-2-2-2-2222-2-2-22-222-22-2-22-22-22-22-2-222−2i2i000000000000−2i2i−2i2i0000−2i−2i2i2i00000000000000000000000
χ352-22-22-12-221-22-1-2-21-22-12-11-211-12-11-2-2-1-2221-111-11-1-221-111-1-12i−2i0000−i3i300−i3i3−i3i32i−2i−ii0000−i−iii00000000000003−33−3000000
χ362-22-22-12-221-22-1-2-21-22-12-11-211-12-11-2-2-1-2221-111-11-1-221-111-1-12i−2i0000i3−i300i3−i3i3−i32i−2i−ii0000−i−iii0000000000000−33−33000000
χ372-22-22-12-221-22-1-2-21-22-12-11-211-12-11-2-2-1-2221-111-11-1-221-111-1-1−2i2i0000−i3i300−i3i3−i3i3−2i2ii−i0000ii−i−i0000000000000−33−33000000
χ382-22-22-12-221-22-1-2-21-22-12-11-211-12-11-2-2-1-2221-111-11-1-221-111-1-1−2i2i0000i3−i300i3−i3i3−i3−2i2ii−i0000ii−i−i00000000000003−33−3000000
χ392-22-2-122-22-2-2-1211-2-22-1-1211-2-2-1-121112-22-1-2-111-11-11-1-2211-1-12i−2i000000000000−ii2i−2i3−300−i−iii3−33−30000000000000−i3i3−i3i300
χ402-22-2-122-22-2-2-1211-2-22-1-1211-2-2-1-121112-22-1-2-111-11-11-1-2211-1-12i−2i000000000000−ii2i−2i−3300−i−iii−33−330000000000000i3−i3i3−i300
χ412-22-2-122-22-2-2-1211-2-22-1-1211-2-2-1-121112-22-1-2-111-11-11-1-2211-1-1−2i2i000000000000i−i−2i2i3−300ii−i−i3−33−30000000000000i3−i3i3−i300
χ422-22-2-122-22-2-2-1211-2-22-1-1211-2-2-1-121112-22-1-2-111-11-11-1-2211-1-1−2i2i000000000000i−i−2i2i−3300ii−i−i−33−330000000000000−i3i3−i3i300
χ4344444-24-4-4-244-244-244-24-2-24-2-2-24-2-24-42-4-4-42-2-2-2-222-4-42222220000000000000000000000000000000000000000000000000
χ4444444-2-244-2-24-244-2-2-2-2-21-2-211-2-21-2-24-2-2-24-21111-2-2-2-2111111000040-2-2-2-2111100000000000000000000000000000000000
χ4544444-2-244-2-24-244-2-2-2-2-21-2-211-2-21-2-24-2-2-24-21111-2-2-2-21111110000-402222-1-1-1-100000000000000000000000000000000000
χ4644444-2-2-4-4-2-24-244-2-2-2-2-21-2-211-2-21-2-2-4222-4211112222-1-1-1-1-1-100000000−2i32i3i3i3−i3−i300000000000000000000000000000000000
χ4744444-2-2-4-4-2-24-244-2-2-2-2-21-2-211-2-21-2-2-4222-4211112222-1-1-1-1-1-1000000002i3−2i3−i3−i3i3i300000000000000000000000000000000000
χ484444-244-4-444-24-2-2444-2-24-2-244-2-24-2-22-4-4-42-4-2-2-2-22222-4-422220000000000000000000000000000000000000000000000000
χ494444-24-2444-2-24-2-24-2-2-21-2-21-2-2-21-2-21-24-2-2-241111-2-211-2-21111000004000000000000-2-2-2-2000011110000000000000000000
χ504444-24-2444-2-24-2-24-2-2-21-2-21-2-2-21-2-21-24-2-2-241111-2-211-2-2111100000-400000000000022220000-1-1-1-10000000000000000000
χ514444-24-2-4-44-2-24-2-24-2-2-21-2-21-2-2-21-2-212-4222-4111122-1-122-1-1-1-100000000000000000000−2i32i30000i3i3−i3−i30000000000000000000
χ524444-24-2-4-44-2-24-2-24-2-2-21-2-21-2-2-21-2-212-4222-4111122-1-122-1-1-1-1000000000000000000002i3−2i30000−i3−i3i3i30000000000000000000
χ534444-2-2444-24-2-2-2-2-2441-2-21-2-2-21-2-21-2-2-244-2-2111111-2-2-2-2111144000000000000-2-2-2-20000111100000000000000000000000
χ544444-2-2444-24-2-2-2-2-2441-2-21-2-2-21-2-21-2-2-244-2-2111111-2-2-2-21111-4-400000000000022220000-1-1-1-100000000000000000000000
χ554444-2-24-4-4-24-2-2-2-2-2441-2-21-2-2-21-2-21-222-4-4221111-1-12222-1-1-1-100000000000000000000003-33-300000000000000000000000
χ564444-2-24-4-4-24-2-2-2-2-2441-2-21-2-2-21-2-21-222-4-4221111-1-12222-1-1-1-10000000000000000000000-33-3300000000000000000000000
χ5744-4-444-200-4-2-4-44-44224-2-2-4-2-22-42242000000-2-2220000000000004i−4i000000000000000000000000000000000−2i2i0000000000
χ5844-4-444-200-4-2-4-44-44224-2-2-4-2-22-42242000000-2-222000000000000−4i4i0000000000000000000000000000000002i−2i0000000000
χ5944-4-44-240024-424-4-2-4-4-24-224-222-42-2-4000000-2-222000000000000000000000000000000000000000000022−220000−2−222000000
χ6044-4-44-240024-424-4-2-4-4-24-224-222-42-2-4000000-2-2220000000000000000000000000000000000000000000−2222000022−2−2000000
χ6144-4-4-24400-442-4-224-4-4-2-242-24-422-4-22000000-2-222000000000000000000000000000000000000000000000−2i22i2000000i2i2−i2−i200
χ6244-4-4-24400-442-4-224-4-4-2-242-24-422-4-22000000-2-2220000000000000000000000000000000000000000000002i2−2i2000000−i2−i2i2i200
χ634-44-444-24-4-4244-4-4-42-24-2-2-42224-2-2-424-4-22-44-222-24-4-22-22-2-2220000000000000000000000000000000000000000000000000
χ644-44-444-2-44-4244-4-4-42-24-2-2-42224-2-2-42-442-24-4-222-2-442-22-222-2-20000000000000000000000000000000000000000000000000
χ654-44-44-244-42-44-2-4-42-44-24-22-422-24-22-4424-4-4-2-222-2-224-4-22-2-2220000000000000000000000000000000000000000000000000
χ664-44-44-2-24-4224-2-4-422-2-2-2122-1-1-2-212242-22-4-21-1-11-22-221-111-1-100000000003-3-3300000000000000000000000000000000000
χ674-44-44-2-24-4224-2-4-422-2-2-2122-1-1-2-212242-22-4-21-1-11-22-221-111-1-10000000000-333-300000000000000000000000000000000000
χ684-44-44-2-2-44224-2-4-422-2-2-2122-1-1-2-2122-4-22-2421-1-112-22-2-11-1-111000000−2i32i300i3−i3i3−i300000000000000000000000000000000000
χ694-44-44-2-2-44224-2-4-422-2-2-2122-1-1-2-2122-4-22-2421-1-112-22-2-11-1-1110000002i3−2i300−i3i3−i3i300000000000000000000000000000000000
χ704-44-4-2444-4-4-4-2422-4-44-2-2422-4-4-2-2422-2-44-424-222-2-22-224-4-2-2220000000000000000000000000000000000000000000000000
χ714-44-4-24-24-4-42-2422-42-2-21-22-122-21-22-1-2-4-22241-1-11-221-1-2211-1-1000000000000000000000000003i−3i−3i3i0000000000000000000
χ724-44-4-24-24-4-42-2422-42-2-21-22-122-21-22-1-2-4-22241-1-11-221-1-2211-1-100000000000000000000000000−3i3i3i−3i0000000000000000000
χ734-44-4-24-2-44-42-2422-42-2-21-22-122-21-22-1242-2-2-41-1-112-2-112-2-1-11100000000000000000023−23000000−33−330000000000000000000
χ744-44-4-24-2-44-42-2422-42-2-21-22-122-21-22-1242-2-2-41-1-112-2-112-2-1-111000000000000000000−23230000003−33−30000000000000000000
χ754-44-4-2-244-42-4-2-2222-441-2-2-12221-2-2-12-224-42-21-1-111-1-22-2211-1-100000000000000000000003i−3i−3i3i00000000000000000000000
χ764-44-4-2-244-42-4-2-2222-441-2-2-12221-2-2-12-224-42-21-1-111-1-22-2211-1-10000000000000000000000−3i3i3i−3i00000000000000000000000
χ774-44-4-2-24-442-4-2-2222-441-2-2-12221-2-2-122-2-44-221-1-11-112-22-2-1-1114i−4i000000000000−2i2i−2i2i0000ii−i−i00000000000000000000000
χ784-44-4-2-24-442-4-2-2222-441-2-2-12221-2-2-122-2-44-221-1-11-112-22-2-1-111−4i4i0000000000002i−2i2i−2i0000−i−iii00000000000000000000000
χ794-4-44444004-4-4-4-44-44-44444-4-44-4-4-4-440000004-44-400000000000000000000000000000000000000000000000000000000000
χ804-4-4444-20042-4-4-44-4-224-2-2422-2-422-4-2000000-22-2200000000000000000000000000000000000000000−2i32i30000000000000000
χ814-4-4444-20042-4-4-44-4-224-2-2422-2-422-4-2000000-22-22000000000000000000000000000000000000000002i3−2i30000000000000000
χ824-4-444-2400-2-4-42-4424-4-24-2-2-42-22-4224000000-22-2200000000000000000000000000000000000000000000000006−6−66000000
χ834-4-444-2400-2-4-42-4424-4-24-2-2-42-22-4224000000-22-220000000000000000000000000000000000000000000000000−666−6000000
χ844-4-44-244004-42-42-2-44-4-2-24-22-4422-42-2000000-22-22000000000000000000000000000000000000000000000000000006−6−6600
χ854-4-44-244004-42-42-2-44-4-2-24-22-4422-42-2000000-22-2200000000000000000000000000000000000000000000000000000−666−600
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
χ8888-8-88-4-4004-4-848-8-444-4-424-42-244-2-4400000022-2-200000000000000000000000000000000000000000000000000000000000
χ8988-8-8-48-400-8-44-8-44844-42-442-444-24-4-200000022-2-200000000000000000000000000000000000000000000000000000000000
χ9088-8-8-4-48004844-44-4-8-82-4-4-2-4-44-2442400000022-2-200000000000000000000000000000000000000000000000000000000000
χ9188-8-8-4-4-4004-444-44-444222-222-2-2-2-22-2000000-1-11100000033−3333−330000000000000000000000000000000000000000000000000
χ9288-8-8-4-4-4004-444-44-444222-222-2-2-2-22-2000000-1-111000000−3333−33330000000000000000000000000000000000000000000000000
χ938-88-8-4-4-48-844-4-44444-4222-2-2-2-2222-2-2-44-444-4-111-12-22-22-2-1-1110000000000000000000000000000000000000000000000000
χ948-88-8-4-4-4-8844-4-44444-4222-2-2-2-2222-2-24-44-4-44-111-1-22-22-2211-1-10000000000000000000000000000000000000000000000000
χ958-8-888-4-400-44-84-884-44-4-42-44-2244-24-40000002-22-200000000000000000000000000000000000000000000000000000000000
χ968-8-88-48-400844-84-4-8-44-42-4-4-24-44-24420000002-22-200000000000000000000000000000000000000000000000000000000000
χ978-8-88-4-4800-4-8444-448-82-4-4244-4-244-2-40000002-22-200000000000000000000000000000000000000000000000000000000000
χ988-8-88-4-4-400-44444-44-442222-2-22-2-2-2-22000000-11-1100000033−33−33330000000000000000000000000000000000000000000000000
χ998-8-88-4-4-400-44444-44-442222-2-22-2-2-2-22000000-11-11000000−333333−330000000000000000000000000000000000000000000000000

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