Finite Group Databasebeta

← Group #13172244

Character table — Group #13172244

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102
size1111222222222222444444444444466888888888888888881212121212121212121212121212121212181824242424242424242424242424242424242436363636363636363636365454727272108
order1222333666666666233366666666644366666666666666664444412121212121212121212121244121212121212121212121212121212121212224441212121212124466124
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111-11-11111-1-1-1-11111-1-11111-1-111111111-1-1-1-1-1-111-111-1-1-1-1-1-1-1-11-1
χ3111111111111111111111111111111111111111111111111-1-111111-1-1111111-1-1-1-1-111-1111111-1-1-1-111111-1-1-11-1-111-1-1-1-11-1-1-1
χ4111111111111111111111111111111111111111111111111-1-1-11-111-1-1-1-1-1-111-1-111-111-1-1-11111-1-1-1-1-1-1-1-1-11-1-1-1-1-1-1-11111-11-11
χ511111111111111111111111111111-1-111111111111111111111-11-1-1111111-1-111111-1-1111-1-1-1-111111111-11-1-1-1-1-1-1-111-1-1-11-1-1
χ611111111111111111111111111111-1-11111111111111111111-1-1-1-1-111-1-1-1-1-1-111-1-11-1-11-1-1-1-1-1-11111-1-1-1-11-1-1-11-1-111-1-1111-1-11
χ711111111111111111111111111111-1-111111111111111111-1-11-11-1-1-1-11111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11111-1-111-111-1-1-1-111-1-111
χ811111111111111111111111111111-1-111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111-1-1111-1
χ91111111111111111-1111111111111111-1-1-1-1-1-1-1-1-1111-1-1-1-11-11-1-1111111-1-111-1-1-1-11-1-1-11-111-1-111-1-111-1-1-111-11-1-111-1-1-1-1-1111
χ101111111111111111-1111111111111111-1-1-1-1-1-1-1-1-1111-1-1-1-11-1-1-111111-1-11111-1-1111-1-1-1-1111-1-111-1-1-1-1111-11-1-1-1-1-1-111111-11-1
χ111111111111111111-1111111111111111-1-1-1-1-1-1-1-1-1111-1-1-1-1-111-1-111-1-111-1-1111111-1-1-111-111-1-1-1-11111-1-1-1-1-11111111111-1-1-1-1
χ121111111111111111-1111111111111111-1-1-1-1-1-1-1-1-1111-1-1-1-1-11-1-1111-1-1-1-1111111-1-1-1-1-11-1111-1-1-1-111-1-11111-11-111-1-1-1-1-1-111-11
χ131111111111111111-1111111111111-1-11-1-1-1-1-1-1-1-1-1111-1-1-1-11-111-1-1-11111-1-1-1-1-1-1-1-1111-11-1-1-11111-1-111-1-111-11-111-1-1-1-11111-1-1
χ141111111111111111-1111111111111-1-11-1-1-1-1-1-1-1-1-1111-1-1-1-11-1-111-1-111-1-111-1-1-1-111111-1-11-1-11111-1-1-1-111-1-1-111111111-1-1-1-1-11
χ151111111111111111-1111111111111-1-11-1-1-1-1-1-1-1-1-1111-1-1-1-1-1111-1-1-1-1-111-1-1-1-11111-11111-1-1-111-1-11111-1-11-11-1-1-1-1-1-111-1-11-111
χ161111111111111111-1111111111111-1-11-1-1-1-1-1-1-1-1-1111-1-1-1-1-11-111-1-1-1-1-1-111-1-111-1-1-1111-11-1-111-1-111-1-111-111-11-1-111-1-111-111-1
χ17222222-122-1-12222-122-1-12-1-122-1-1-1-100-122-122-1-1-1-1-1-1-1-1-1-1-12220200-1-122-1-1002222200-1-120000-1-1-1-1-1-1-1-1020000000-1-1000-100
χ18222222-122-1-12222-122-1-12-1-122-1-1-1-100-122-122-1-1-1-1-1-1-1-1-1-1-122-20-200-1-1-2-2110022-2-2200-11-20000-1-1-1-111110-2000000011000100
χ19222222-122-1-12222-122-1-12-1-122-1-1-1-100-122-122-1-1-1-1-1-1-1-1-1-1-1-2-2202001122-1-100-2-2-2-2-2001-1200001111-1-1-1-10-2000000011000100
χ20222222-122-1-12222-122-1-12-1-122-1-1-1-100-122-122-1-1-1-1-1-1-1-1-1-1-1-2-2-20-20011-2-21100-2-222-20011-2000011111111020000000-1-1000-100
χ21222222-122-1-12222-1-22-1-12-1-122-1-1-1-100-1-2-21-2-21111-1-1-111112-220-200-1-1221100-2-2-2-22001-1-20000-1-111-1-11102000000011000-100
χ22222222-122-1-12222-1-22-1-12-1-122-1-1-1-100-1-2-21-2-21111-1-1-111112-2-20200-1-1-2-2-1-100-2-2222001120000-1-11111-1-10-20000000-1-1000100
χ23222222-122-1-12222-1-22-1-12-1-122-1-1-1-100-1-2-21-2-21111-1-1-11111-2220-200112211002222-200-1-1-2000011-1-1-1-1110-20000000-1-1000100
χ24222222-122-1-12222-1-22-1-12-1-122-1-1-1-100-1-2-21-2-21111-1-1-11111-22-2020011-2-2-1-10022-2-2-200-112000011-1-111-1-102000000011000-100
χ2522222-12-1-122222-122-12-1-12-1-1-122-1-122-12-12-1-122-1-1-1-1-1-1-1-1-100222-1-100-1-12222000002-102-1-1-1-1-10000-1-1-1-12000200-1-10000-1000
χ2622222-12-1-122222-122-12-1-12-1-1-122-1-122-12-12-1-122-1-1-1-1-1-1-1-1-100-22-2-1-10011-2-222000002-10-21-1-1-1-100001111-2000-2001100001000
χ2722222-12-1-122222-122-12-1-12-1-1-122-1-1-2-2-12-12-1-122-1-1-1-1-1-1-1-1-1002-221100-1-122-2-200000-2102-111110000-1-1-1-1-2000-2001100001000
χ2822222-12-1-122222-122-12-1-12-1-1-122-1-1-2-2-12-12-1-122-1-1-1-1-1-1-1-1-100-2-2-2110011-2-2-2-200000-210-211111000011112000200-1-10000-1000
χ2922222-12-1-122222-12-2-12-1-12-1-1-122-1-122-1-21-211-2-211-1-1-11111002-2-2-1-100-1-1-2-22200000-21021-1-1110000-1-111-2000200-1-100001000
χ3022222-12-1-122222-12-2-12-1-12-1-1-122-1-122-1-21-211-2-211-1-1-1111100-2-22-1-10011222200000-210-2-1-1-111000011-1-12000-200110000-1000
χ3122222-12-1-122222-12-2-12-1-12-1-1-122-1-1-2-2-1-21-211-2-211-1-1-111110022-21100-1-1-2-2-2-2000002-102111-1-10000-1-1112000-200110000-1000
χ3222222-12-1-122222-12-2-12-1-12-1-1-122-1-1-2-2-1-21-211-2-211-1-1-1111100-22211001122-2-2000002-10-2-111-1-1000011-1-1-2000200-1-100001000
χ332222-1222222-1-1-1222-1-12-1-12-1-1-1-12222-1-122-1-1-1-122-1-1-1-1-1-1-12202022220000-1-1-1-100-1-12200-1-1-1-1-1-1-1-1000000220-1-100000000-10
χ342222-1222222-1-1-1222-1-12-1-12-1-1-1-12222-1-122-1-1-1-122-1-1-1-1-1-1-1-2-202022-2-20000-1-111001-12-200-1-1-1-11111000000-2-20110000000010
χ352222-1222222-1-1-1222-1-12-1-12-1-1-1-122-2-2-1-122-1-1-1-122-1-1-1-1-1-1-1220-20-2-222000011-1-100-11-22001111-1-1-1-1000000-2-20110000000010
χ362222-1222222-1-1-1222-1-12-1-12-1-1-1-122-2-2-1-122-1-1-1-122-1-1-1-1-1-1-1-2-20-20-2-2-2-2000011110011-2-20011111111000000220-1-100000000-10
χ372222-1222222-1-1-122-2-1-12-1-12-1-1-1-12222-11-2-21111-2-2-1-1-111112-20-2022220000-1-11100-11-2-200-1-111-1-1110000002-201100000000-10
χ382222-1222222-1-1-122-2-1-12-1-12-1-1-1-12222-11-2-21111-2-2-1-1-11111-220-2022-2-20000-1-1-1-10011-2200-1-11111-1-1000000-220-1-10000000010
χ392222-1222222-1-1-122-2-1-12-1-12-1-1-1-122-2-2-11-2-21111-2-2-1-1-111112-2020-2-2220000111100-1-12-20011-1-1-1-111000000-220-1-10000000010
χ402222-1222222-1-1-122-2-1-12-1-12-1-1-1-122-2-2-11-2-21111-2-2-1-1-11111-22020-2-2-2-2000011-1-1001-1220011-1-111-1-10000002-201100000000-10
χ412-22-22222-2-2-2-22-2-2202222-2-2-2-22-22-22i−2i20000000002-2-20000000002i−2i0000002i−2i002-20000002i−2i00000000000000000002-22i−2i0000
χ422-22-22222-2-2-2-22-2-2202222-2-2-2-22-22-22i−2i20000000002-2-20000000002i−2i0000002i−2i00-220000002i−2i0000000000000000000-22−2i2i0000
χ432-22-22222-2-2-2-22-2-2202222-2-2-2-22-22-2−2i2i20000000002-2-2000000000−2i2i000000−2i2i002-2000000−2i2i00000000000000000002-2−2i2i0000
χ442-22-22222-2-2-2-22-2-2202222-2-2-2-22-22-2−2i2i20000000002-2-2000000000−2i2i000000−2i2i00-22000000−2i2i0000000000000000000-222i−2i0000
χ4544444-2-2-2-2-2-2444-2-24-2-21-2-21-2-2-2-2110014-2-2-2-2-2-2111111111004040000-2-2-2-20000000000-2-200000000111100000000000000000
χ4644444-2-2-2-2-2-2444-2-24-2-21-2-21-2-2-2-2110014-2-2-2-2-2-211111111100-40-40000222200000000002200000000-1-1-1-100000000000000000
χ4744444-2-2-2-2-2-2444-2-2-4-2-21-2-21-2-2-2-211001-4222222-1-1111-1-1-1-10040-40000-2-2220000000000-220000000011-1-100000000000000000
χ4844444-2-2-2-2-2-2444-2-2-4-2-21-2-21-2-2-2-211001-4222222-1-1111-1-1-1-100-404000022-2-200000000002-200000000-1-11100000000000000000
χ494444-24-244-2-2-2-2-24-24-21-2-21-2-2-211-2-2001-24-2-2-211-2-211111114400000-2-2000000-2-200-200-20000001111000000000000000000000
χ504444-24-244-2-2-2-2-24-24-21-2-21-2-2-211-2-2001-24-2-2-211-2-21111111-4-4000002200000022002002000000-1-1-1-1000000000000000000000
χ514444-24-244-2-2-2-2-24-2-4-21-2-21-2-2-211-2-20012-4222-1-122111-1-1-1-14-400000-2-20000002200-200200000011-1-1000000000000000000000
χ524444-24-244-2-2-2-2-24-2-4-21-2-21-2-2-211-2-20012-4222-1-122111-1-1-1-1-440000022000000-2-200200-2000000-1-111000000000000000000000
χ534444-2-24-2-244-2-2-2-2441-2-21-2-211-2-2-2-2441-2-2411-2-2-2-2111111100040-2-2000000-2-200000-2-200011110000000000000000000000000
χ544444-2-24-2-244-2-2-2-2441-2-21-2-211-2-2-2-2-4-41-2-2411-2-2-2-21111111000-4022000000220000022000-1-1-1-10000000000000000000000000
χ554444-2-24-2-244-2-2-2-24-41-2-21-2-211-2-2-2-244122-4-1-12222111-1-1-1-1000-40-2-2000000-2-2000002200011-1-10000000000000000000000000
χ564444-2-24-2-244-2-2-2-24-41-2-21-2-211-2-2-2-2-4-4122-4-1-12222111-1-1-1-100040220000002200000-2-2000-1-1110000000000000000000000000
χ5744-4-4444-444-44-4-4-4-40444-4-444-4-44-4-4004000000000-44-40000000000000000000000000000000000000000000000000000000000
χ5844-4-444-2-44-224-4-4-4204-2-2-42-24-42-22200-20000000002-2200000000000000023−23000000000000000000000023−2300000000000000000
χ5944-4-444-2-44-224-4-4-4204-2-2-42-24-42-22200-20000000002-22000000000000000−23230000000000000000000000−232300000000000000000
χ6044-4-44-242-24-44-4-42-40-24-22-4-2-22-442200-20000000002-22000000000000023−23000000000000000000000023−230000000000000000000
χ6144-4-44-242-24-44-4-42-40-24-22-4-2-22-442200-20000000002-220000000000000−23230000000000000000000000−23230000000000000000000
χ6244-4-44-2-22-2-224-4-4220-2-21221-222-2-1-100100000003-3-11-133-3-300000000023−2323−2300000000000000000000−33−3300000000000000000
χ6344-4-44-2-22-2-224-4-4220-2-21221-222-2-1-100100000003-3-11-133-3-3000000000−2323−2323000000000000000000003−33−300000000000000000
χ6444-4-44-2-22-2-224-4-4220-2-21221-222-2-1-10010000000-33-11-1-3-33300000000023−23−232300000000000000000000−333−300000000000000000
χ6544-4-44-2-22-2-224-4-4220-2-21221-222-2-1-10010000000-33-11-1-3-333000000000−232323−23000000000000000000003−3−3300000000000000000
χ6644-4-4-244-444-4-222-4-40-2-24224-222-2-4-400-20000000002-22000000000000000000000000000000000000000000000023−230000000000
χ6744-4-4-244-444-4-222-4-40-2-24224-222-2-4-400-20000000002-220000000000000000000000000000000000000000000000−23230000000000
χ684-44-444-24-422-44-4-4-204-2-2422-4-4-22-2200-2000000000-2220000000000000000000004-4000000000000000000000000000-22000000
χ694-44-444-24-422-44-4-4-204-2-2422-4-4-22-2200-2000000000-222000000000000000000000-440000000000000000000000000002-2000000
χ704-44-44-24-22-4-4-44-4240-24-2-2-42224-4-224i−4i-2000000000-222000000000−2i2i0000004i−4i0000000000−2i2i000000000000000000000000000
χ714-44-44-24-22-4-4-44-4240-24-2-2-42224-4-22−4i4i-2000000000-2220000000002i−2i000000−4i4i00000000002i−2i000000000000000000000000000
χ724-44-4-2444-4-4-42-22-440-2-24-22-422-224-44i−4i-2000000000-2220000000004i−4i000000−2i2i0000000000−2i2i000000000000000000000000000
χ734-44-4-2444-4-4-42-22-440-2-24-22-422-224-4−4i4i-2000000000-222000000000−4i4i0000002i−2i00000000002i−2i000000000000000000000000000
χ744-44-4-2-24-22-4-42-222401-2-2122-1-1-22-224i−4i10003-300001-1-13-33-300000−2i2i000000−2i2i0000000000i−i3i−3i0000000000000000000000000
χ754-44-4-2-24-22-4-42-222401-2-2122-1-1-22-224i−4i1000-3300001-1-1-33-3300000−2i2i000000−2i2i0000000000i−i−3i3i0000000000000000000000000
χ764-44-4-2-24-22-4-42-222401-2-2122-1-1-22-22−4i4i10003-300001-1-13-33-3000002i−2i0000002i−2i0000000000−ii−3i3i0000000000000000000000000
χ774-44-4-2-24-22-4-42-222401-2-2122-1-1-22-22−4i4i1000-3300001-1-1-33-33000002i−2i0000002i−2i0000000000−ii3i−3i0000000000000000000000000
χ784-4-44444-4-4-44-4-444-40444-44-4-44-4-4-44004000000000-4-440000000000000000000000000000000000000000000000000000000000
χ794-4-4444-2-4-42-2-4-444204-2-2-4-22-44222-200-200000000022-20000000000023−230000000000000000000023−2300000000000000000000000
χ804-4-4444-2-4-42-2-4-444204-2-2-4-22-44222-200-200000000022-200000000000−232300000000000000000000−232300000000000000000000000
χ814-4-444-2422-44-4-44-2-40-24-22422-2-4-42-200-200000000022-2000000000000000000000000000000000000000000000000−2i32i300000000
χ824-4-444-2422-44-4-44-2-40-24-22422-2-4-42-200-200000000022-20000000000000000000000000000000000000000000000002i3−2i300000000
χ834-4-44-244-4-4-4422-24-40-2-242-2-42-222-4400-200000000022-2000000000000000000023−230000000000000023−23000000000000000000000
χ844-4-44-244-4-4-4422-24-40-2-242-2-42-222-4400-200000000022-20000000000000000000−232300000000000000−2323000000000000000000000
χ854-4-44-24-2-4-42-222-2420-21-22122-2-1-12-2001000003-300-1-113-3-33000000023−2300000023−23000000000000−33−33000000000000000000000
χ864-4-44-24-2-4-42-222-2420-21-22122-2-1-12-2001000003-300-1-113-3-330000000−2323000000−23230000000000003−33−3000000000000000000000
χ874-4-44-24-2-4-42-222-2420-21-22122-2-1-12-200100000-3300-1-11-333-3000000023−23000000−2323000000000000−333−3000000000000000000000
χ884-4-44-24-2-4-42-222-2420-21-22122-2-1-12-200100000-3300-1-11-333-30000000−232300000023−230000000000003−3−33000000000000000000000
χ898888-4-4-4-4-4-4-4-4-4-4-4-4822222222222200-1-4-4-4222222-1-1-1-1-1-1-1000000000000000000000000000000000000000000000000000000
χ908888-4-4-4-4-4-4-4-4-4-4-4-4-822222222222200-1444-2-2-2-2-2-2-1-1-11111000000000000000000000000000000000000000000000000000000
χ9188-8-8-48-4-88-44-444-840-42-44-2-4-44-2244002000000000-22-20000000000000000000000000000000000000000000000000000000000
χ9288-8-8-4-484-48-8-4444-802-4-4-24-42-24-444002000000000-22-20000000000000000000000000000000000000000000000000000000000
χ9388-8-8-4-4-44-4-44-444440222-2-222-2-22-2-200-100000006-61-11-3-333000000000000000000000000000000000000000000000000000000
χ9488-8-8-4-4-44-4-44-444440222-2-222-2-22-2-200-10000000-661-1133-3-3000000000000000000000000000000000000000000000000000000
χ958-88-88-4-4-4444-88-84-40-4-42-44-244-442-20020000000002-2-20000000000000000000000000000000000000000000000000000000000
χ968-88-8-48-48-8444-44-8-40-42-4-4-24442-2-440020000000002-2-20000000000000000000000000000000000000000000000000000000000
χ978-88-8-4-4-4-44444-444-402222-2-2-2-22-22-200-10006-60000-111-33-33000000000000000000000000000000000000000000000000000000
χ988-88-8-4-4-4-44444-444-402222-2-2-2-22-22-200-1000-660000-1113-33-3000000000000000000000000000000000000000000000000000000
χ998-8-888-4-4444-4-8-88-440-4-424-4-24-444-22002000000000-2-220000000000000000000000000000000000000000000000000000000000
χ1008-8-88-4-4844-8844-4-4-802-4-4-2-44-22444-4002000000000-2-220000000000000000000000000000000000000000000000000000000000
χ1018-8-88-4-4-4444-444-4-440222-22-2-22-2-2-2200-1000006-60011-1-333-3000000000000000000000000000000000000000000000000000000
χ1028-8-88-4-4-4444-444-4-440222-22-2-22-2-2-2200-100000-660011-13-3-33000000000000000000000000000000000000000000000000000000

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