Finite Group Databasebeta

← Group #13172280

Character table — Group #13172280

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102
size111122222222222244444444444444466888888888888888812121212121212121212121212181824242424242424242424242424242424242424243636363636363636363636363654547272108
order12223336666666662333666666666664436666666666666664444412121212121212124412121212121212121212121212121212121212124444412121212121212124412124
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111-11-111-1-11111-1-1111-11-11-111111111-1-1-1-11-1-11-111-1-1-1-1-1-1-1-11-1-1
χ311111111111111111111111111111111111111111111111111-11-11-1-1111111-1-111-11-11-111111-1-1-1-11111-11-1-11-1-111-1-1-1-1-1-1-11-1
χ411111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-11-1-1-1-1-1-1111111-1-11
χ51111111111111111111111111111111-1-11111111111111111-111111111-1-1-1-111-1-1111111-1-1-1-111111111-1-11-1-1-1-1-1-11111-1-1-1-1-1
χ61111111111111111111111111111111-1-11111111111111111-11-11-111-1-1-1-1-1-1-1-1-1-11-11-11-1-1-1-1-11111-1-1-1-1-11-1-11-1-111-1-1-1-111-111
χ71111111111111111111111111111111-1-11111111111111111-1-11-11-1-111-1-1-1-1-1-1-1-1-11-11-11-1-1-1-1-1-1-1-111111-1-11-111-1-1-1-1-1-1111-11
χ81111111111111111111111111111111-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111-1-111-1
χ91111111111111111-1111-1-1111111111111-1-1-1-1-1-1-1-1111-1-1-1-1-111-1-11111111111-1-111-1-1-1-111-1-111-1-111-1-111-1-1-1111111-1-111-1-1-1
χ101111111111111111-1111-1-1111111111111-1-1-1-1-1-1-1-1111-1-1-1-1-11-1-1111-1-11111-1-1-1-11-1-11-1111-1-111-1-1-1-1111-11-1111-1-1-1-111-1-1-111
χ111111111111111111-1111-1-1111111111111-1-1-1-1-1-1-1-1111-1-1-1-1-1-111-1-1-1111111-1-1-1-1-111-11-111-1-1-1-11111-1-1-1111-1-1-111-1-111-1-11-11
χ121111111111111111-1111-1-1111111111111-1-1-1-1-1-1-1-1111-1-1-1-1-1-1-111-1-1-1-1111111-1-1-1-1111111-1-1-1-111-1-111-1-1-111-1-1-1-111-1-11111-1
χ131111111111111111-1111-1-1111111111-1-11-1-1-1-1-1-1-1-1111-1-1-1-1111-1-11111-1-1-1-1111111-1-1-1-1-1-11111-1-111-1-1-1-1-111-1-1-1-111-1-1-1-1111
χ141111111111111111-1111-1-1111111111-1-11-1-1-1-1-1-1-1-1111-1-1-1-111-1-1111-1-1-1-1-1-1-1-1111-1-11-11-1-11111-1-1-1-111-1111-1-1-111-1-111111-1-1
χ151111111111111111-1111-1-1111111111-1-11-1-1-1-1-1-1-1-1111-1-1-1-11-111-1-1-111-1-1-1-1-1-111-111-11-1-1-111-1-11111-1-11-11-1111-1-1-1-11111-11-1
χ161111111111111111-1111-1-1111111111-1-11-1-1-1-1-1-1-1-1111-1-1-1-11-1-111-1-1-1-1-1-1-1-11111-1-11111-1-111-1-111-1-11111-1-1-1111111-1-1-1-1-1-11
χ17222222-1222-122-1-1222-1-1222-1-122-1-1-1-122-12-122-1-1-1-1-1-1-1-1-1-1-12020200-1-122-1-1002-1020-102-1-1-1-10000-1-1-1-10200200-1-10000000-10
χ18222222-1222-122-1-1222-1-1222-1-122-1-1-1-122-12-122-1-1-1-1-1-1-1-1-1-1-120-20-2001122-1-1002-10-2010-2-1-1-1-1000011110-200-20011000000010
χ19222222-1222-122-1-1222-1-1222-1-122-1-1-1-1-2-2-12-122-1-1-1-1-1-1-1-1-1-1-1-2020200-1-1-2-21100-21020-10211110000-1-1-1-10-200-20011000000010
χ20222222-1222-122-1-1222-1-1222-1-122-1-1-1-1-2-2-12-122-1-1-1-1-1-1-1-1-1-1-1-20-20-20011-2-21100-210-2010-21111000011110200200-1-10000000-10
χ21222222-1222-122-1-12-22-1-1-2-22-1-122-1-1-1-122-1-21-2-21111-1-1-11111-2020-200-1-122-1-100-2102010-2-1-1110000-1-1110200-200-1-1000000010
χ22222222-1222-122-1-12-22-1-1-2-22-1-122-1-1-1-122-1-21-2-21111-1-1-11111-20-202001122-1-100-210-20-102-1-111000011-1-10-200200110000000-10
χ23222222-1222-122-1-12-22-1-1-2-22-1-122-1-1-1-1-2-2-1-21-2-21111-1-1-111112020-200-1-1-2-211002-102010-211-1-10000-1-1110-200200110000000-10
χ24222222-1222-122-1-12-22-1-1-2-22-1-122-1-1-1-1-2-2-1-21-2-21111-1-1-1111120-2020011-2-211002-10-20-10211-1-1000011-1-10200-200-1-1000000010
χ2522222-1222-12-1-12222-12-122-12-1-1-122-1-122-1-12-1-122-1-1-1-1-1-1-1-1-122020-1-100-1-12200-1220-1020-1-1-1-1-1-1-1-1000020020-1-100000000-100
χ2622222-1222-12-1-12222-12-122-12-1-1-122-1-122-1-12-1-122-1-1-1-1-1-1-1-1-12-20-201100-1-12200-12-2010-20-1-1-1-111110000-200-201100000000100
χ2722222-1222-12-1-12222-12-122-12-1-1-122-1-1-2-2-1-12-1-122-1-1-1-1-1-1-1-1-1-22020-1-10011-2-2001-220-10201111-1-1-1-10000-200-201100000000100
χ2822222-1222-12-1-12222-12-122-12-1-1-122-1-1-2-2-1-12-1-122-1-1-1-1-1-1-1-1-1-2-20-20110011-2-2001-2-2010-2011111111000020020-1-100000000-100
χ2922222-1222-12-1-1222-2-12-1-2-2-12-1-1-122-1-122-11-211-2-211-1-1-11111-220-20-1-100-1-122001-22010-20-1-111-1-1110000200-20-1-100000000100
χ3022222-1222-12-1-1222-2-12-1-2-2-12-1-1-122-1-122-11-211-2-211-1-1-11111-2-20201100-1-122001-2-20-1020-1-11111-1-10000-200201100000000-100
χ3122222-1222-12-1-1222-2-12-1-2-2-12-1-1-122-1-1-2-2-11-211-2-211-1-1-11111220-20-1-10011-2-200-122010-2011-1-1-1-1110000-200201100000000-100
χ3222222-1222-12-1-1222-2-12-1-2-2-12-1-1-122-1-1-2-2-11-211-2-211-1-1-111112-2020110011-2-200-12-20-102011-1-111-1-10000200-20-1-100000000100
χ332222-122-1-1222222-12-1-12-1-1-1-12-1-1-1-12200-122-1-1-1-122-1-1-1-1-1-1-102222222200002200-1-122-1-10000-1-1-1-1-1-1-1-1002000000-1-1-1-100000
χ342222-122-1-1222222-12-1-12-1-1-1-12-1-1-1-12200-122-1-1-1-122-1-1-1-1-1-1-102-22-222-2-20000-2-200-112-2-110000-1-1-1-1111100-2000000111100000
χ352222-122-1-1222222-12-1-12-1-1-1-12-1-1-1-12200-122-1-1-1-122-1-1-1-1-1-1-10-22-22-2-2220000-2-2001-1-221-100001111-1-1-1-100-2000000111100000
χ362222-122-1-1222222-12-1-12-1-1-1-12-1-1-1-12200-122-1-1-1-122-1-1-1-1-1-1-10-2-2-2-2-2-2-2-20000220011-2-211000011111111002000000-1-1-1-100000
χ372222-122-1-1222222-1-2-1-1211-1-12-1-1-1-12200-1-2-21111-2-2-1-1-11111022-2-2222200002200-1-1-2-2110000-1-111-1-11100-2000000-1-11100000
χ382222-122-1-1222222-1-2-1-1211-1-12-1-1-1-12200-1-2-21111-2-2-1-1-1111102-2-2222-2-20000-2-200-11-221-10000-1-11111-1-100200000011-1-100000
χ392222-122-1-1222222-1-2-1-1211-1-12-1-1-1-12200-1-2-21111-2-2-1-1-111110-222-2-2-2220000-2-2001-12-2-11000011-1-1-1-11100200000011-1-100000
χ402222-122-1-1222222-1-2-1-1211-1-12-1-1-1-12200-1-2-21111-2-2-1-1-111110-2-222-2-2-2-2000022001122-1-1000011-1-111-1-100-2000000-1-11100000
χ412-22-2222-2-2-2-22-22-22022200-2-222-22-2-2-22i−2i2000000002-2-200000000000002i−2i2i−2i2-2000000002i−2i00000000000000000002-2002i−2i000
χ422-22-2222-2-2-2-22-22-22022200-2-222-22-2-2-22i−2i2000000002-2-200000000000002i−2i2i−2i-22000000002i−2i0000000000000000000-2200−2i2i000
χ432-22-2222-2-2-2-22-22-22022200-2-222-22-2-2-2−2i2i2000000002-2-20000000000000−2i2i−2i2i2-200000000−2i2i00000000000000000002-200−2i2i000
χ442-22-2222-2-2-2-22-22-22022200-2-222-22-2-2-2−2i2i2000000002-2-20000000000000−2i2i−2i2i-2200000000−2i2i0000000000000000000-22002i−2i000
χ4544444-2-244-2-2-2-2-2-244-2-2144-2-21-2-2-2-211441-2-2-2-2-2-2111111111400000000-2-2-2-200-2-2000000111100000000000000000000000000
χ4644444-2-244-2-2-2-2-2-244-2-2144-2-21-2-2-2-211-4-41-2-2-2-2-2-2111111111-40000000022220022000000-1-1-1-100000000000000000000000000
χ4744444-2-244-2-2-2-2-2-24-4-2-21-4-4-2-21-2-2-2-211441222222-1-1111-1-1-1-1-400000000-2-2-2-2002200000011-1-100000000000000000000000000
χ4844444-2-244-2-2-2-2-2-24-4-2-21-4-4-2-21-2-2-2-211-4-41222222-1-1111-1-1-1-1400000000222200-2-2000000-1-11100000000000000000000000000
χ494444-24-2-2-24-244-2-2-24-21-2-2-2-21-2-2-211-2-20014-2-2-211-2-211111110040400-2-2000000000-20-20-2000000001111000000000000000000
χ504444-24-2-2-24-244-2-2-24-21-2-2-2-21-2-2-211-2-20014-2-2-211-2-2111111100-40-400220000000002020200000000-1-1-1-1000000000000000000
χ514444-24-2-2-24-244-2-2-2-4-21-222-21-2-2-211-2-2001-4222-1-122111-1-1-1-10040-400-2-2000000000-202020000000011-1-1000000000000000000
χ524444-24-2-2-24-244-2-2-2-4-21-222-21-2-2-211-2-2001-4222-1-122111-1-1-1-100-404002200000000020-20-200000000-1-111000000000000000000
χ534444-2-24-2-2-24-2-244-241-2-2-2-21-2-211-2-2-2-2001-2411-2-2-2-2111111104040-2-20000000000-20-20-20000011110000000000000000000000
χ544444-2-24-2-2-24-2-244-241-2-2-2-21-2-211-2-2-2-2001-2411-2-2-2-211111110-40-402200000000002020200000-1-1-1-10000000000000000000000
χ554444-2-24-2-2-24-2-244-2-41-2-2221-2-211-2-2-2-20012-4-1-12222111-1-1-1-1040-40-2-20000000000-202020000011-1-10000000000000000000000
χ564444-2-24-2-2-24-2-244-2-41-2-2221-2-211-2-2-2-20012-4-1-12222111-1-1-1-10-404022000000000020-20-200000-1-1110000000000000000000000
χ5744-4-4444-4444-4-4-4-4-4044400-4-4-4-44-444-400400000000-44-4000000000000000000000000000000000000000000000000000000000
χ5844-4-444-2-444-2-4-422-404-2-200-422-442-2-2200-2000000002-22000000000000000000000000000000000000000000000023−23000000000
χ5944-4-444-2-444-2-4-422-404-2-200-422-442-2-2200-2000000002-220000000000000000000000000000000000000000000000−2323000000000
χ6044-4-44-24-44-2422-4-4-40-24-2002-422-2-44-2200-2000000002-220000000000000000000000000000000000000000000023−2300000000000
χ6144-4-44-24-44-2422-4-4-40-24-2002-422-2-44-2200-2000000002-2200000000000000000000000000000000000000000000−232300000000000
χ6244-4-4-2442-244-4-4-4-420-2-240022-42-22-24-400-2000000002-220000000000000000000000000000000000000000000000000023−2300000
χ6344-4-4-2442-244-4-4-4-420-2-240022-42-22-24-400-2000000002-2200000000000000000000000000000000000000000000000000−232300000
χ644-44-444-2-4-4-424-4-22404-2-200-42-24-4-22224i−4i-200000000-22200000000000004i−4i−2i2i0000000000−2i2i0000000000000000000000000000
χ654-44-444-2-4-4-424-4-22404-2-200-42-24-4-2222−4i4i-200000000-2220000000000000−4i4i2i−2i00000000002i−2i0000000000000000000000000000
χ664-44-44-24-4-42-4-224-440-24-2002-4-2-224-4224i−4i-200000000-2220000000000000−2i2i4i−4i0000000000−2i2i0000000000000000000000000000
χ674-44-44-24-4-42-4-224-440-24-2002-4-2-224-422−4i4i-200000000-22200000000000002i−2i−4i4i00000000002i−2i0000000000000000000000000000
χ684-44-44-2-2-4-422-22-2240-2-2100221-22-22-1-14i−4i10000003-31-1-133-3-3000000000−2i2i−2i2i0000000000i−i3i−3i00000000000000000000000000
χ694-44-44-2-2-4-422-22-2240-2-2100221-22-22-1-14i−4i1000000-331-1-1-3-333000000000−2i2i−2i2i0000000000i−i−3i3i00000000000000000000000000
χ704-44-44-2-2-4-422-22-2240-2-2100221-22-22-1-1−4i4i10000003-31-1-133-3-30000000002i−2i2i−2i0000000000−ii−3i3i00000000000000000000000000
χ714-44-44-2-2-4-422-22-2240-2-2100221-22-22-1-1−4i4i1000000-331-1-1-3-3330000000002i−2i2i−2i0000000000−ii3i−3i00000000000000000000000000
χ724-44-4-24422-4-44-44-4-20-2-2400224-22-22-4-400-200000000-222000000000000000004-400000000000000000000000000000-220000000
χ734-44-4-24422-4-44-44-4-20-2-2400224-22-22-4-400-200000000-22200000000000000000-44000000000000000000000000000002-20000000
χ744-4-444444-4-4-4-44-44-404440044-4-4-4-4-4-4400400000000-4-44000000000000000000000000000000000000000000000000000000000
χ754-4-4444-24-4-42-442-2-404-2-2004-22-4-4222-200-20000000022-20000000000023−23000000000000000000000023−2300000000000000000000
χ764-4-4444-24-4-42-442-2-404-2-2004-22-4-4222-200-20000000022-200000000000−23230000000000000000000000−232300000000000000000000
χ774-4-444-244-42-42-2-44-40-24-200-24222-4-42-200-20000000022-200000000023−230000000000000000000023−23000000000000000000000000
χ784-4-444-244-42-42-2-44-40-24-200-24222-4-42-200-20000000022-2000000000−232300000000000000000000−2323000000000000000000000000
χ794-4-44-244-22-4-4-44-4420-2-24−2i32i3-2-2-42222-4400-200−2i32i3−2i32i30022-2−2i32i3−2i32i300000000000000000000000000000000000000000000000000000
χ804-4-44-244-22-4-4-44-4420-2-242i3−2i3-2-2-42222-4400-2002i3−2i32i3−2i30022-22i3−2i32i3−2i300000000000000000000000000000000000000000000000000000
χ814-4-44-24-2-22-42-442-220-21-2−2i32i3-21222-1-12-200100−2i32i3i3−i300-1-11i3−i3i3−i3000000023−230000000000000000000000−333i−3i000000000000000000
χ824-4-44-24-2-22-42-442-220-21-2−2i32i3-21222-1-12-200100−2i32i3i3−i300-1-11i3−i3i3−i30000000−232300000000000000000000003−3−3i3i000000000000000000
χ834-4-44-24-2-22-42-442-220-21-22i3−2i3-21222-1-12-2001002i3−2i3−i3i300-1-11−i3i3−i3i3000000023−230000000000000000000000−33−3i3i000000000000000000
χ844-4-44-24-2-22-42-442-220-21-22i3−2i3-21222-1-12-2001002i3−2i3−i3i300-1-11−i3i3−i3i30000000−232300000000000000000000003−33i−3i000000000000000000
χ854-4-44-2-24-222-42-2-44201-2-2−2i32i31-22-1-1222-200100i3−i3−2i32i300-1-11i3−i3i3−i30000023−2300000000000000000000−333i−3i0000000000000000000000
χ864-4-44-2-24-222-42-2-44201-2-2−2i32i31-22-1-1222-200100i3−i3−2i32i300-1-11i3−i3i3−i300000−2323000000000000000000003−3−3i3i0000000000000000000000
χ874-4-44-2-24-222-42-2-44201-2-22i3−2i31-22-1-1222-200100−i3i32i3−2i300-1-11−i3i3−i3i30000023−2300000000000000000000−33−3i3i0000000000000000000000
χ884-4-44-2-24-222-42-2-44201-2-22i3−2i31-22-1-1222-200100−i3i32i3−2i300-1-11−i3i3−i3i300000−2323000000000000000000003−33i−3i0000000000000000000000
χ898888-4-4-4-4-4-4-4-4-4-4-4-48222-4-422222222200-1-4-4222222-1-1-1-1-1-1-100000000000000000000000000000000000000000000000000000
χ908888-4-4-4-4-4-4-4-4-4-4-4-4-82224422222222200-144-2-2-2-2-2-2-1-1-1111100000000000000000000000000000000000000000000000000000
χ9188-8-88-4-4-88-4-44444-80-4-420044-24-44-42-200200000000-22-2000000000000000000000000000000000000000000000000000000000
χ9288-8-8-48-44-48-4-8-84440-42-4004-244-4-22-4400200000000-22-2000000000000000000000000000000000000000000000000000000000
χ9388-8-8-4-484-4-4844-8-8402-4-400-244-224-4-4400200000000-22-2000000000000000000000000000000000000000000000000000000000
χ9488-8-8-4-4-44-4-4-444444022200-2-2-2-22-222-200-1000000001-11−3i33i33i3−3i300000000000000000000000000000000000000000000000000000
χ9588-8-8-4-4-44-4-4-444444022200-2-2-2-22-222-200-1000000001-113i3−3i3−3i33i300000000000000000000000000000000000000000000000000000
χ968-88-8-48-444-848-8-44-40-42-4004-2-4-442-244002000000002-2-2000000000000000000000000000000000000000000000000000000000
χ978-88-8-4-48444-8-448-8-402-4-400-24-42-2-4444002000000002-2-2000000000000000000000000000000000000000000000000000000000
χ988-88-8-4-4-44444-44-44-4022200-2-222-22-2-2-200-10000006-6-111-3-33300000000000000000000000000000000000000000000000000000
χ998-88-8-4-4-44444-44-44-4022200-2-222-22-2-2-200-1000000-66-11133-3-300000000000000000000000000000000000000000000000000000
χ1008-8-888-4-48-8444-44-4-80-4-4200-4-4-24444-2200200000000-2-22000000000000000000000000000000000000000000000000000000000
χ1018-8-88-4-4-4-44444-44-440222−4i34i322-2-2-2-2-2-2200-1002i3−2i32i3−2i30011-1−i3i3−i3i300000000000000000000000000000000000000000000000000000
χ1028-8-88-4-4-4-44444-44-4402224i3−4i322-2-2-2-2-2-2200-100−2i32i3−2i32i30011-1i3−i3i3−i300000000000000000000000000000000000000000000000000000

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