Finite Group Databasebeta

← Group #13171783

Character table — Group #13171783

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102
size111122222222222244444444444444466888888888888888812121212121212121212121212181824242424242424242424242424242424242424243636363636363636363636363654547272108
order122233366666666623336666666666622366666666666666622444666666121244666666666121212121212121212121224444661212121212124412124
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111-111-1111111-1-1-1-11-1-11111-1-1111-111111-1-11-1-11-111-1-1-1-1-1-1-1-11-1-1
χ31111111111111111111111111111111111111111111111111-111-111111-1-111-1-1-11111-1-1111-1-11111-1-111-111-1-1-1-111-1-1-1-1-1-1-11-1
χ41111111111111111111111111111111111111111111111111-1-11-1-11111-1-1-1-111-1-1-111-1-1-1-11-1-1-1111-1-1-1-1-1-1-1-11-1-1-1-1111111-1-11
χ51111111111111111111111111111111-1-1111111111111111111-111-1-1-1-1111111111-1-11111-1111-1-1-11111-1-1-1-11-1-1-1-11111-1-1-1-1-1
χ61111111111111111111111111111111-1-111111111111111111-1-11-1-1-1-1-111-1-1-1-11-1-1-1-111-1-1-111-1-1-1-111-1-1-111-1-1-1-111-1-1-1-111-111
χ71111111111111111111111111111111-1-11111111111111111-11-1-11-1-1-1-1-1-111-1-1-111-1-1-1-111-1-1-11-1-1-1-1-1111-1-11-111-1-1-1-1-1-1111-11
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
χ91111111111111111-1111-1-1111111111111-1-1-1-1-1-1-1-1111-1-1-1-111-1-1-1111111-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-1-111-1-1111-1-111-1-1-1-1-111
χ101111111111111111-1111-1-1111111111111-1-1-1-1-1-1-1-1111-1-1-1-11-1-1-1111111111111-1-11111-1-1-1-1-11-1-1-1-1-1111-11-1-11111-1-11111-1-1-1
χ111111111111111111-1111-1-1111111111111-1-1-1-1-1-1-1-1111-1-1-1-1-11-11-11111-1-1-1-111-11111-1-111-111-1-1-1-111-1-1-11-11-1-1-1-1-1-1-1111111-1
χ121111111111111111-1111-1-1111111111111-1-1-1-1-1-1-1-1111-1-1-1-1-1-1-1111111-1-111-1-1-1-1-111-1-1-1-1-1111-1-1-11111-1-1111-1-11111-1-1-1-11-11
χ131111111111111111-1111-1-1111111111-1-11-1-1-1-1-1-1-1-1111-1-1-1-1111-1-1-1-1-1-111-1-1-1-1111-1-111111-1-1-1111-1-1-1-1-1-1111-1-11111-1-1111-1-1
χ141111111111111111-1111-1-1111111111-1-11-1-1-1-1-1-1-1-1111-1-1-1-11-11-11-1-1-1-11111111-1-1-1-111-1-11-1-11111-1-111-11-11-1-1-1-1-1-1-111-1-1111
χ151111111111111111-1111-1-1111111111-1-11-1-1-1-1-1-1-1-1111-1-1-1-1-1111-1-1-1-1-1-1-1-1-111-111-1-1-1-111111-111111-1-11-11-1-11111-1-111-1-1-1-11
χ161111111111111111-1111-1-1111111111-1-11-1-1-1-1-1-1-1-1111-1-1-1-1-1-1111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-11111111111111-1-1111-1-111-1-111-11-1
χ17222222-122-1-12-122222-1-12222-1-1-1-12-1-122-12-122-1-1-1-1-1-1-1-1-1-1-12022022-1-1-1-10000200-1-1-1-100-1-1202-1-1-1-10020020-1-100000000-100
χ18222222-122-1-12-122222-1-12222-1-1-1-12-1-122-12-122-1-1-1-1-1-1-1-1-1-1-1-202-2022-1-1110000-200-1-11100-11-202-1-11100-200-201100000000100
χ19222222-122-1-12-122222-1-12222-1-1-1-12-1-1-2-2-12-122-1-1-1-1-1-1-1-1-1-1-120-220-2-211-1-1000020011-1-1001-120-211-1-100-200-201100000000100
χ20222222-122-1-12-122222-1-12222-1-1-1-12-1-1-2-2-12-122-1-1-1-1-1-1-1-1-1-1-1-20-2-20-2-211110000-20011110011-20-211110020020-1-100000000-100
χ21222222-122-1-12-1222-22-1-1-2-222-1-1-1-12-1-122-1-21-2-21111-1-1-1111120-2-2022-1-1-1-10000200-1-1-1-10011-20-2111100200-20-1-100000000100
χ22222222-122-1-12-1222-22-1-1-2-222-1-1-1-12-1-122-1-21-2-21111-1-1-11111-20-22022-1-1110000-200-1-111001-120-211-1-100-200201100000000-100
χ23222222-122-1-12-1222-22-1-1-2-222-1-1-1-12-1-1-2-2-1-21-2-21111-1-1-11111202-20-2-211-1-1000020011-1-100-11-202-1-11100-200201100000000-100
χ24222222-122-1-12-1222-22-1-1-2-222-1-1-1-12-1-1-2-2-1-21-2-21111-1-1-11111-20220-2-211110000-200111100-1-1202-1-1-1-100200-20-1-100000000100
χ2522222-122-12222-1-122-12-122-1-122-1-1-12-122-1-12-1-122-1-1-1-1-1-1-1-1-102202-1-12200-1-10002-1-1-100-1-12002-1-1-100-1-10220000-1-10000000-10
χ2622222-122-12222-1-122-12-122-1-122-1-1-12-122-1-12-1-122-1-1-1-1-1-1-1-1-10-220-2-1-1220011000-21-1-10011200-2-1-1-100110-2-2000011000000010
χ2722222-122-12222-1-122-12-122-1-122-1-1-12-1-2-2-1-12-1-122-1-1-1-1-1-1-1-1-102-20211-2-200-1-10002-11100-1-1-200211100-1-10-2-2000011000000010
χ2822222-122-12222-1-122-12-122-1-122-1-1-12-1-2-2-1-12-1-122-1-1-1-1-1-1-1-1-10-2-20-211-2-20011000-21110011-200-211100110220000-1-10000000-10
χ2922222-122-12222-1-12-2-12-1-2-2-1-122-1-1-12-122-11-211-2-211-1-1-1111102-20-2-1-12200110002-1-1-100-1-1-200-2111001102-20000110000000-10
χ3022222-122-12222-1-12-2-12-1-2-2-1-122-1-1-12-122-11-211-2-211-1-1-111110-2-202-1-12200-1-1000-21-1-10011-200211100-1-10-220000-1-1000000010
χ3122222-122-12222-1-12-2-12-1-2-2-1-122-1-1-12-1-2-2-11-211-2-211-1-1-111110220-211-2-200110002-11100-1-1200-2-1-1-100110-220000-1-1000000010
χ3222222-122-12222-1-12-2-12-1-2-2-1-122-1-1-12-1-2-2-11-211-2-211-1-1-111110-220211-2-200-1-1000-211100112002-1-1-100-1-102-20000110000000-10
χ332222-122-1222-1222-12-1-12-1-1-1-1-1-122-1-1200-122-1-1-1-122-1-1-1-1-1-1-1220220000222222-1-1200-1-1-1-102-1-1000-1-1-1-1000020000-1-1-1-100000
χ342222-122-1222-1222-12-1-12-1-1-1-1-1-122-1-1200-122-1-1-1-122-1-1-1-1-1-1-12-202-2000022-2-2-2-2-11-200-1-11102-11000-1-1110000-20000111100000
χ352222-122-1222-1222-12-1-12-1-1-1-1-1-122-1-1200-122-1-1-1-122-1-1-1-1-1-1-1-220-220000-2-222-2-21-120011-1-10-21-100011-1-10000-20000111100000
χ362222-122-1222-1222-12-1-12-1-1-1-1-1-122-1-1200-122-1-1-1-122-1-1-1-1-1-1-1-2-20-2-20000-2-2-2-22211-20011110-2110001111000020000-1-1-1-100000
χ372222-122-1222-1222-1-2-1-1211-1-1-1-122-1-1200-1-2-21111-2-2-1-1-11111220-2-2000022-2-2-2-2-1-1200-1-1-1-10-2110001111000020000-1-11100000
χ382222-122-1222-1222-1-2-1-1211-1-1-1-122-1-1200-1-2-21111-2-2-1-1-111112-20-220000222222-11-200-1-1110-21-100011-1-10000-2000011-1-100000
χ392222-122-1222-1222-1-2-1-1211-1-1-1-122-1-1200-1-2-21111-2-2-1-1-11111-2202-20000-2-2-2-2221-120011-1-102-11000-1-1110000-2000011-1-100000
χ402222-122-1222-1222-1-2-1-1211-1-1-1-122-1-1200-1-2-21111-2-2-1-1-11111-2-20220000-2-222-2-211-200111102-1-1000-1-1-1-1000020000-1-11100000
χ4122-2-22222-22-2-2-22-2-20222002-22-2-2-2-2-222-22000000002-2-20000000002-22-200002i−2i0002-2000000000000000000000000002i−2i2i−2i000
χ4222-2-22222-22-2-2-22-2-20222002-22-2-2-2-2-222-22000000002-2-20000000002-22-20000−2i2i0002-200000000000000000000000000−2i2i−2i2i000
χ4322-2-22222-22-2-2-22-2-20222002-22-2-2-2-2-22-222000000002-2-2000000000-22-2200002i−2i000-22000000000000000000000000002i−2i−2i2i000
χ4422-2-22222-22-2-2-22-2-20222002-22-2-2-2-2-22-222000000002-2-2000000000-22-220000−2i2i000-2200000000000000000000000000−2i2i2i−2i000
χ4544444-2-24-2-2-24-2-2-244-2-2144-2-2-2-211-2-21441-2-2-2-2-2-211111111100400-2-2-2-2000000000110000-2000-2110000000000000000000000
χ4644444-2-24-2-2-24-2-2-244-2-2144-2-2-2-211-2-21-4-41-2-2-2-2-2-211111111100-4002222000000000-1-1000020002-1-10000000000000000000000
χ4744444-2-24-2-2-24-2-2-24-4-2-21-4-4-2-2-2-211-2-21441222222-1-1111-1-1-1-100-400-2-2-2-200000000011000020002-1-10000000000000000000000
χ4844444-2-24-2-2-24-2-2-24-4-2-21-4-4-2-2-2-211-2-21-4-41222222-1-1111-1-1-1-1004002222000000000-1-10000-2000-2110000000000000000000000
χ494444-24-2-24-2-2-2-244-24-21-2-2-2-2-211-2-2-21-20014-2-2-211-2-21111111400400000-2-20000-2000011000-2-200001100000000000000000000
χ504444-24-2-24-2-2-2-244-24-21-2-2-2-2-211-2-2-21-20014-2-2-211-2-21111111-400-40000022000020000-1-1000220000-1-100000000000000000000
χ514444-24-2-24-2-2-2-244-2-4-21-222-2-211-2-2-21-2001-4222-1-122111-1-1-1-1400-400000-2-20000-2000011000220000-1-100000000000000000000
χ524444-24-2-24-2-2-2-244-2-4-21-222-2-211-2-2-21-2001-4222-1-122111-1-1-1-1-40040000022000020000-1-1000-2-200001100000000000000000000
χ534444-2-24-2-244-24-2-2-241-2-2-2-211-2-2-2-21-2-2001-2411-2-2-2-2111111104004000000-2-2000-2-2000011000-20000011000000000000000000
χ544444-2-24-2-244-24-2-2-241-2-2-2-211-2-2-2-21-2-2001-2411-2-2-2-211111110-400-400000022000220000-1-1000200000-1-1000000000000000000
χ554444-2-24-2-244-24-2-2-2-41-2-22211-2-2-2-21-2-20012-4-1-12222111-1-1-1-10400-400000022000-2-2000011000200000-1-1000000000000000000
χ564444-2-24-2-244-24-2-2-2-41-2-22211-2-2-2-21-2-20012-4-1-12222111-1-1-1-10-4004000000-2-2000220000-1-1000-20000011000000000000000000
χ5744-4-444-24-4-22-424-4-404-2-2004-4-2222-42-24-4-200000000-2220000000004-4-22000000000-22000000000000000000000000000000000
χ5844-4-444-24-4-22-424-4-404-2-2004-4-2222-42-2-44-200000000-222000000000-442-20000000002-2000000000000000000000000000000000
χ5944-4-44-24424-4-4-4-22-40-24-200-224-4222-4-24-4-200000000-222000000000-224-4000000000-22000000000000000000000000000000000
χ6044-4-44-24424-4-4-4-22-40-24-200-224-4222-4-2-44-200000000-2220000000002-2-440000000002-2000000000000000000000000000000000
χ6144-4-44-2-242-22-42-22-40-2-2100-22-22-1-12214-410000003-31-1-133-3-300000-22-220000000001-10000000003-30000000000000000000000
χ6244-4-44-2-242-22-42-22-40-2-2100-22-22-1-12214-41000000-331-1-1-3-33300000-22-220000000001-1000000000-330000000000000000000000
χ6344-4-44-2-242-22-42-22-40-2-2100-22-22-1-1221-4410000003-31-1-133-3-3000002-22-2000000000-11000000000-330000000000000000000000
χ6444-4-44-2-242-22-42-22-40-2-2100-22-22-1-1221-441000000-331-1-1-3-333000002-22-2000000000-110000000003-30000000000000000000000
χ6544-4-4-244-2-44-42-44-420-2-2400-22-22-4-422400-200000000-222000000000000000004i−4i0000000000000000000000000000000−2i2i00000
χ6644-4-4-244-2-44-42-44-420-2-2400-22-22-4-422400-200000000-22200000000000000000−4i4i00000000000000000000000000000002i−2i00000
χ674-44-4444-4-4-444-4-44-4044400-4-4-4-44-444-400400000000-44-4000000000000000000000000000000000000000000000000000000000
χ684-44-444-2-4-42-242-44-404-2-200-4-422-224-2200-2000000002-220000000000000−2i32i3000000000−2i32i30000000000000000000000000000000
χ694-44-444-2-4-42-242-44-404-2-200-4-422-224-2200-2000000002-2200000000000002i3−2i30000000002i3−2i30000000000000000000000000000000
χ704-44-44-24-42-444-42-2-40-24-20022-4-4-22-24200-2000000002-22000000000000000−2i32i300000000000000000000−2i32i3000000000000000000
χ714-44-44-24-42-444-42-2-40-24-20022-4-4-22-24200-2000000002-220000000000000002i3−2i3000000000000000000002i3−2i3000000000000000000
χ724-44-4-2442-4-44-2-4-4420-2-24−2i32i322224-4-2-2-400-200−2i32i3−2i32i3002-22−2i32i3−2i32i300000000000000000000000000000000000000000000000000000
χ734-44-4-2442-4-44-2-4-4420-2-242i3−2i322224-4-2-2-400-2002i3−2i32i3−2i3002-222i3−2i32i3−2i300000000000000000000000000000000000000000000000000000
χ744-44-4-24-22-42-2-22-4420-21-2−2i32i322-1-1-22-21200100−2i32i3i3−i300-11-1i3−i3i3−i3000000000−2i32i3000000000i3−i30000000003-300000000000000000000
χ754-44-4-24-22-42-2-22-4420-21-2−2i32i322-1-1-22-21200100−2i32i3i3−i300-11-1i3−i3i3−i30000000002i3−2i3000000000−i3i3000000000-3300000000000000000000
χ764-44-4-24-22-42-2-22-4420-21-22i3−2i322-1-1-22-212001002i3−2i3−i3i300-11-1−i3i3−i3i3000000000−2i32i3000000000i3−i3000000000-3300000000000000000000
χ774-44-4-24-22-42-2-22-4420-21-22i3−2i322-1-1-22-212001002i3−2i3−i3i300-11-1−i3i3−i3i30000000002i3−2i3000000000−i3i30000000003-300000000000000000000
χ784-44-4-2-2422-44-2-42-2201-2-2−2i32i3-1-122-221-2200100i3−i3−2i32i300-11-1i3−i3i3−i300000000000−2i32i30000000003-3000000000i3−i3000000000000000000
χ794-44-4-2-2422-44-2-42-2201-2-2−2i32i3-1-122-221-2200100i3−i3−2i32i300-11-1i3−i3i3−i3000000000002i3−2i3000000000-33000000000−i3i3000000000000000000
χ804-44-4-2-2422-44-2-42-2201-2-22i3−2i3-1-122-221-2200100−i3i32i3−2i300-11-1−i3i3−i3i300000000000−2i32i3000000000-33000000000i3−i3000000000000000000
χ814-44-4-2-2422-44-2-42-2201-2-22i3−2i3-1-122-221-2200100−i3i32i3−2i300-11-1−i3i3−i3i3000000000002i3−2i30000000003-3000000000−i3i3000000000000000000
χ824-4-44444-44-4-4-44-4-44044400-44-44-44-4-4-400400000000-4-44000000000000000000000000000000000000000000000000000000000
χ834-4-4444-2-4422-4-2-4-4404-2-200-442-22-2-42200-20000000022-200000000000000000000000000000000000000000000−2i32i300000000000
χ844-4-4444-2-4422-4-2-4-4404-2-200-442-22-2-42200-20000000022-2000000000000000000000000000000000000000000002i3−2i300000000000
χ854-4-444-24-4-2-4-4-442240-24-2002-2-442-22-4200-20000000022-2000000000000000000000000000000000000000000000023−23000000000
χ864-4-444-24-4-2-4-4-442240-24-2002-2-442-22-4200-20000000022-20000000000000000000000000000000000000000000000−2323000000000
χ874-4-44-24424-4-424-4-4-20-2-24002-22-2-4422-400-20000000022-2000000000000000000000000000000000000000000000000−2i32i30000000
χ884-4-44-24424-4-424-4-4-20-2-24002-22-2-4422-400-20000000022-20000000000000000000000000000000000000000000000002i3−2i30000000
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
χ9188-8-8-48-4-4-8-44448-840-42-400-442-2444-2-4002000000002-2-2000000000000000000000000000000000000000000000000000000000
χ9288-8-8-4-48-448-84-8-44402-4-4002-2-4444-24-4002000000002-2-2000000000000000000000000000000000000000000000000000000000
χ9388-8-8-4-4-4-44-4444-4440222002-22-2-2-2-2-2200-10000006-6-111-3-33300000000000000000000000000000000000000000000000000000
χ9488-8-8-4-4-4-44-4444-4440222002-22-2-2-2-2-2200-1000000-66-11133-3-300000000000000000000000000000000000000000000000000000
χ958-88-88-4-4-844-4844-4-80-4-420044442-2-4-4-200200000000-22-2000000000000000000000000000000000000000000000000000000000
χ968-88-8-4-4-4444-4-444-440222−4i34i3-2-2-2-22-222-200-1002i3−2i32i3−2i3001-11−i3i3−i3i300000000000000000000000000000000000000000000000000000
χ978-88-8-4-4-4444-4-444-4402224i3−4i3-2-2-2-22-222-200-100−2i32i3−2i32i3001-11i3−i3i3−i300000000000000000000000000000000000000000000000000000
χ988-8-888-4-4-8-444-8-44480-4-42004-44-4-2244-200200000000-2-22000000000000000000000000000000000000000000000000000000000
χ998-8-88-48-448444-4-8-8-40-42-4004-4-224-44-2400200000000-2-22000000000000000000000000000000000000000000000000000000000
χ1008-8-88-4-484-4-8-84844-402-4-400-224-44-4-24400200000000-2-22000000000000000000000000000000000000000000000000000000000
χ1018-8-88-4-4-44-4444-444-4022200-22-22-22-2-2-200-10000000011-1−3i33i33i3−3i300000000000000000000000000000000000000000000000000000
χ1028-8-88-4-4-44-4444-444-4022200-22-22-22-2-2-200-10000000011-13i3−3i3−3i33i300000000000000000000000000000000000000000000000000000

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