Finite Group Databasebeta

← Group #13172683

Character table — Group #13172683

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111
size11112222222222224444444444444446666888888888888888812121212121212121212121212121212121212121818181818181818181818182424242424242424242424242424242436363636363636367272108108
order122233366666666623336666666666622443666666666666666244466666612121212121212121212222222446666666661212121212121212121212246666121261224
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111-1-1111111111111-1-1-1-11111-1-1-1-11111111111-1-11111-1-1-1-1-1-1-1-111-1-1-1-1-1-1
χ3111111111111111111111111111111111-1-11111111111111111-11111111-1-111-1-1-1-11111-1-1-1-1-1-111-1-1-1-1-111-1-111111-1-111111-1-1-1-1-1111-1-1-1
χ4111111111111111111111111111111111-1-11111111111111111-11-1-11111-1-111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-111-1-11-1-111-1-1-1-1-1-1-1111-1-1-1-1-1111
χ51111111111111111111111111111111-1-11111111111111111111-111-1-1-1-111-1-111111111-1-1-1-111-1-1-1-1-1-11-1-111-111-1-1111111-1111-1-1-1-1-11-1-1
χ61111111111111111111111111111111-1-11111111111111111111-1-1-1-1-1-1-111-1-11111-1-1-1-1-1-1-1-1-1-111-1-1-1-11-1-111-1-1-1-1-111-1-1-1-11-1-1-1-1-1111-111
χ71111111111111111111111111111111-1-1-1-11111111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-111-1-1-1-11111-1-1-1-111-1-1-1-111
χ81111111111111111111111111111111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1
χ91111111111111111-1111-1-111111111111111-1-1-1-1-1-1-1-1111-1-1-1-1-1-11-11111-1-1-1-1111111-1-111-1-111-1-1-1-1-1-1-111-1-1-11-1-1-11111-1-11-11111-1-11-11-1
χ101111111111111111-1111-1-111111111111111-1-1-1-1-1-1-1-1111-1-1-1-1-1-1-111111-1-1-1-11111-1-11111-1-1-1-111-1-1-1-1-111-1-1-1-11-1-111-1-111-11-1-11111-11-11
χ111111111111111111-1111-1-111111111111-1-11-1-1-1-1-1-1-1-1111-1-1-1-11-11-1111111-1-1-1-1-1-111-1-1-1-111-1-1-1-1111111111-11-1-1-1-1-111-1-111-1-1-1-1-1-111-11
χ121111111111111111-1111-1-111111111111-1-11-1-1-1-1-1-1-1-1111-1-1-1-11-1-11111111-1-1-1-1-1-1-1-111-1-1111111111111111-1-11-1-1-1-1-1-111-1-111-1-111-1-11-1
χ131111111111111111-1111-1-1111111111-1-1111-1-1-1-1-1-1-1-1111-1-1-1-1-111-1-1-1-1-1-1-111111111-1-1-1-11111111111-1-1-1-1-111-1111111-1-1-1-111-1-111-1-1-11
χ141111111111111111-1111-1-1111111111-1-1111-1-1-1-1-1-1-1-1111-1-1-1-1-11-11-1-1-1-1-1-1111111-1-111-1-111-1-1-1-11111-1-1-1-1-11-111111-1-11111-1-1-1-1-1-1111-1
χ151111111111111111-1111-1-1111111111-1-1-1-11-1-1-1-1-1-1-1-1111-1-1-1-1111-1-1-1-1-11111-1-1-1-111-1-111-1-1-1-111-1-1-1-11-1-11111-111-1-111-1-1-11-1-11111-111-1
χ161111111111111111-1111-1-1111111111-1-1-1-11-1-1-1-1-1-1-1-1111-1-1-1-111-11-1-1-1-11111-1-1-1-1-1-11111-1-111-1-1-1-1-1-11-1-1111-1111-1-1-1-1111-11111-1-11-1-11
χ17222222-122-1-122-12222-1-1-1-12-1-1-1-122-1-12222-12222-1-1-1-1-1-1-1-1-1-1-1220022-1-1-1-1-1-122-1-1000022220000-1-1-1-12-1-1-1-1200-1-1-1-100000000-1-1000000
χ18222222-122-1-122-12222-1-1-1-12-1-1-1-122-1-122-2-2-12222-1-1-1-1-1-1-1-1-1-1-1-220022-1-111-1-1-2-2110000-2-2-2-200001111-2-1-111200-1-1110000000011000000
χ19222222-122-1-122-12222-1-1-1-12-1-1-1-122-1-1-2-222-12222-1-1-1-1-1-1-1-1-1-1-12-200-2-211-1-11122-1-10000-2-2-2-200001111211-1-1-20011-1-10000000011000000
χ20222222-122-1-122-12222-1-1-1-12-1-1-1-122-1-1-2-2-2-2-12222-1-1-1-1-1-1-1-1-1-1-1-2-200-2-2111111-2-211000022220000-1-1-1-1-21111-200111100000000-1-1000000
χ21222222-122-1-122-122-22-1-1112-1-1-1-122-1-12222-1-2-2-2-21111-1-1-11111-2-20022-1-1111122-1-1000022-2-200001111-2-1-111-20011-1-100000000-1-1000000
χ22222222-122-1-122-122-22-1-1112-1-1-1-122-1-122-2-2-1-2-2-2-21111-1-1-111112-20022-1-1-1-111-2-2110000-2-2220000-1-1-1-12-1-1-1-1-20011110000000011000000
χ23222222-122-1-122-122-22-1-1112-1-1-1-122-1-1-2-222-1-2-2-2-21111-1-1-11111-2200-2-21111-1-122-1-10000-2-2220000-1-1-1-1-21111200-1-1-1-10000000011000000
χ24222222-122-1-122-122-22-1-1112-1-1-1-122-1-1-2-2-2-2-1-2-2-2-21111-1-1-111112200-2-211-1-1-1-1-2-211000022-2-200001111211-1-1200-1-11100000000-1-1000000
χ2522222-122-1222-122-12-12-122-122-1-1-1-12-10022-12-1-1-122-1-1-1-1-1-1-1-1-1202200002200-1-122-1-122000022000000-100-1-102-100-1-1-1-1-1-102-1-100000-100
χ2622222-122-1222-122-12-12-122-122-1-1-1-12-10022-12-1-1-122-1-1-1-1-1-1-1-1-120-2-200002200-1-12211-2-20000-2-2000000-100-1-10-2100-1-111110-21100000100
χ2722222-122-1222-122-12-12-122-122-1-1-1-12-100-2-2-12-1-1-122-1-1-1-1-1-1-1-1-1-20220000-2-20011-2-2-1-1220000-2-20000001001102-10011-1-1-1-10-21100000100
χ2822222-122-1222-122-12-12-122-122-1-1-1-12-100-2-2-12-1-1-122-1-1-1-1-1-1-1-1-1-20-2-20000-2-20011-2-211-2-2000022000000100110-210011111102-1-100000-100
χ2922222-122-1222-122-1-2-12-1-2-2-122-1-1-1-12-10022-1-2111-2-211-1-1-11111-202-20000-2-200-1-122-1-1-2-20000220000001001102100-1-1-1-1110-2-1-100000100
χ3022222-122-1222-122-1-2-12-1-2-2-122-1-1-1-12-10022-1-2111-2-211-1-1-11111-20-220000-2-200-1-12211220000-2-2000000100110-2-100-1-111-1-1021100000-100
χ3122222-122-1222-122-1-2-12-1-2-2-122-1-1-1-12-100-2-2-1-2111-2-211-1-1-11111202-20000220011-2-2-1-1-2-20000-2-2000000-100-1-10210011-1-111021100000-100
χ3222222-122-1222-122-1-2-12-1-2-2-122-1-1-1-12-100-2-2-1-2111-2-211-1-1-1111120-220000220011-2-21122000022000000-100-1-10-2-1001111-1-10-2-1-100000100
χ332222-122-1222-122-122-1-1222-1-1-122-1-1-122200-1-12-1-1-1-122-1-1-1-1-1-1-10222-1-1220022000022-1-10000002200000-1-100-1-12-1-100-1-1-1-1200000-1-1-1000
χ342222-122-1222-122-122-1-1222-1-1-122-1-1-122200-1-12-1-1-1-122-1-1-1-1-1-1-102-2-2-1-12200220000-2-211000000-2-200000-1-100-11-2-1-1001111-200000111000
χ352222-122-1222-122-122-1-1222-1-1-122-1-1-12-2-200-1-12-1-1-1-122-1-1-1-1-1-1-10-22211-2-200-2-2000022-1-1000000-2-20000011001-121100-1-1-1-1-200000111000
χ362222-122-1222-122-122-1-1222-1-1-122-1-1-12-2-200-1-12-1-1-1-122-1-1-1-1-1-1-10-2-2-211-2-200-2-20000-2-2110000002200000110011-211001111200000-1-1-1000
χ372222-122-1222-122-12-2-1-12-2-2-1-1-122-1-1-122200-11-21111-2-2-1-1-111110-22-2-1-12200-2-200002211000000-2-200000-1-1001-1-21100-1-11120000011-1000
χ382222-122-1222-122-12-2-1-12-2-2-1-1-122-1-1-122200-11-21111-2-2-1-1-111110-2-22-1-12200-2-20000-2-2-1-10000002200000-1-100112110011-1-1-200000-1-11000
χ392222-122-1222-122-12-2-1-12-2-2-1-1-122-1-1-12-2-200-11-21111-2-2-1-1-11111022-211-2-200220000221100000022000001100-1-1-2-1-100-1-111-200000-1-11000
χ402222-122-1222-122-12-2-1-12-2-2-1-1-122-1-1-12-2-200-11-21111-2-2-1-1-1111102-2211-2-200220000-2-2-1-1000000-2-2000001100-112-1-10011-1-120000011-1000
χ4122-2-2222-2-2-2-2222-2-2022200-2-2-2-2-22-2222-22-22000000002-2-2000000002-22-200002-22-200002-2000000000002-200000002-2000000002-2000000
χ4222-2-2222-2-2-2-2222-2-2022200-2-2-2-2-22-2222-2-222000000002-2-2000000002-22-20000-22-220000-22000000000002-20000000-2200000000-22000000
χ4322-2-2222-2-2-2-2222-2-2022200-2-2-2-2-22-222-222-22000000002-2-200000000-22-2200002-22-20000-2200000000000-2200000002-200000000-22000000
χ4422-2-2222-2-2-2-2222-2-2022200-2-2-2-2-22-222-22-222000000002-2-200000000-22-220000-22-2200002-200000000000-220000000-22000000002-2000000
χ4522-2-222-1-2-21122-1-2-202-1-1−i3i3-211112-2-1-12-22-2-10000−i3i3−i3i3-111−i3−i3i3i300002-2-11−i3i3−i3i32-2-1100002-2000000−i3−i3i3i30-11−i3i3000−i3i3-1100000000-11000000
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χ4722-2-222-1-2-21122-1-2-202-1-1−i3i3-211112-2-1-1-222-2-10000−i3i3−i3i3-111−i3−i3i3i30000-221-1−i3i3i3−i32-2-110000-22000000i3i3−i3−i301-1−i3i3000i3−i3-11000000001-1000000
χ4822-2-222-1-2-21122-1-2-202-1-1−i3i3-211112-2-1-1-22-22-10000−i3i3−i3i3-111−i3−i3i3i30000-221-1i3−i3i3−i3-221-100002-2000000−i3−i3i3i301-1i3−i3000i3−i31-100000000-11000000
χ4922-2-222-1-2-21122-1-2-202-1-1i3−i3-211112-2-1-12-22-2-10000i3−i3i3−i3-111i3i3−i3−i300002-2-11i3−i3i3−i32-2-1100002-2000000i3i3−i3−i30-11i3−i3000i3−i3-1100000000-11000000
χ5022-2-222-1-2-21122-1-2-202-1-1i3−i3-211112-2-1-12-2-22-10000i3−i3i3−i3-111i3i3−i3−i300002-2-11−i3i3i3−i3-221-10000-22000000−i3−i3i3i30-11−i3i3000i3−i31-1000000001-1000000
χ5122-2-222-1-2-21122-1-2-202-1-1i3−i3-211112-2-1-1-222-2-10000i3−i3i3−i3-111i3i3−i3−i30000-221-1i3−i3−i3i32-2-110000-22000000−i3−i3i3i301-1i3−i3000−i3i3-11000000001-1000000
χ5222-2-222-1-2-21122-1-2-202-1-1i3−i3-211112-2-1-1-22-22-10000i3−i3i3−i3-111i3i3−i3−i30000-221-1−i3i3−i3i3-221-100002-2000000i3i3−i3−i301-1−i3i3000−i3i31-100000000-11000000
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χ904-4-444-244-2-44-42-4-420-24-200-2-442-222-420000-20000000022-20000000000000000000023−230000000000000000000000000023−2300000000000000
χ914-4-444-244-2-44-42-4-420-24-200-2-442-222-420000-20000000022-200000000000000000000−232300000000000000000000000000−232300000000000000
χ924-4-44-244-24-442-4-42-40-2-2400-22-2-44222-40000-20000000022-2000000000000000000000023−230000000000000000000000000023−23000000000000
χ934-4-44-244-24-442-4-42-40-2-2400-22-2-44222-40000-20000000022-20000000000000000000000−232300000000000000000000000000−2323000000000000
χ944-4-44-2-24-2-2-4422-42201-2-20012-22-2-1-12200001003-30000-1-113-33-3000000000000000023−2323−23000000000000000000000000−33−33000000000000
χ954-4-44-2-24-2-2-4422-42201-2-20012-22-2-1-12200001003-30000-1-113-33-30000000000000000−2323−23230000000000000000000000003−33−3000000000000
χ964-4-44-2-24-2-2-4422-42201-2-20012-22-2-1-1220000100-330000-1-11-33-33000000000000000023−23−2323000000000000000000000000−333−3000000000000
χ974-4-44-2-24-2-2-4422-42201-2-20012-22-2-1-1220000100-330000-1-11-33-330000000000000000−232323−230000000000000000000000003−3−33000000000000
χ988888-4-4-4-4-4-4-4-4-4-4-4-48222-4-42222222220000-1-4-4222222-1-1-1-1-1-1-1000000000000000000000000000000000000000000000000000000000000
χ998888-4-4-4-4-4-4-4-4-4-4-4-4-8222442222222220000-144-2-2-2-2-2-2-1-1-11111000000000000000000000000000000000000000000000000000000000000
χ10088-8-8-4-4844-8-8-4-484402-4-400-244442-2-4-400002000000002-2-20000000000000000000000000000000000000000000000000000000000000000
χ10188-8-8-4-4-44444-4-4-4440222−4i34i3-2-2-2-2-22-2220000-100002i3−2i32i3−2i3-111−i3−i3i3i3000000000000000000000000000000000000000000000000000000000000
χ10288-8-8-4-4-44444-4-4-44402224i3−4i3-2-2-2-2-22-2220000-10000−2i32i3−2i32i3-111i3i3−i3−i3000000000000000000000000000000000000000000000000000000000000
χ1038-88-88-4-4-84-44-8448-40-4-42004-442-24-44-20000200000000-22-20000000000000000000000000000000000000000000000000000000000000000
χ1048-88-8-48-44-8-444-84-480-42-40042-2-444-4-240000200000000-22-20000000000000000000000000000000000000000000000000000000000000000
χ1058-88-8-4-48448-844-8-4-402-4-400-2-44-44-22440000200000000-22-20000000000000000000000000000000000000000000000000000000000000000
χ1068-88-8-4-4-444-44444-4-4022200-22-22-2-22-2-20000-1000000001-11−3i33i33i3−3i3000000000000000000000000000000000000000000000000000000000000
χ1078-88-8-4-4-444-44444-4-4022200-22-22-2-22-2-20000-1000000001-113i3−3i3−3i33i3000000000000000000000000000000000000000000000000000000000000
χ1088-8-888-4-48-44-4-844-840-4-4200-44-4-22444-20000200000000-2-220000000000000000000000000000000000000000000000000000000000000000
χ1098-8-88-48-4-484-44-844-80-42-400-4-224-444-240000200000000-2-220000000000000000000000000000000000000000000000000000000000000000
χ1108-8-88-4-4-4-4-44-4444440222002-22-22-2-2-2-20000-1006-6000011-1-33-33000000000000000000000000000000000000000000000000000000000000
χ1118-8-88-4-4-4-4-44-4444440222002-22-22-2-2-2-20000-100-66000011-13-33-3000000000000000000000000000000000000000000000000000000000000

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