Finite Group Databasebeta

← Group #11793998

Character table — Group #11793998

Order 1152.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90
size111122222222222222444444444444444444448888888888888888888888242424242424242424242424242424242424242424242424363636367272
order12442223344466121212123666666666121212121212121212124466121212121212121212121212121212121212224444446666121212121212121212121212888888
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111-11-111-1-111-1-111-1-11111-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111111111111111111111-11-11-1-111-1-111-1-111-1-1-1-11111-1-1-1-1-1-1
χ4111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ511111111111111111111111111111111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111
χ611111111111111111111111111111111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-11-1-1-11111-1-111-1-1-1-1-1-111111111-1-1
χ711111111111111111111111111111111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1111-1-1-1-111-1-1111111-1-1-1-11111-1-1
χ811111111111111111111111111111111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-111
χ922222222-12222-122-1-1-12-12-1-1-1-12-1222-1-1-1-1-1-1-122-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-10202002200-1-100-1-10000-1-1-1-1000000
χ1022222222-12222-122-1-1-12-12-1-1-1-12-1222-1-1-1-1-1-1-122-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-10-20-200-2-20011001100001111000000
χ1122222222-12222-122-1-1-12-12-1-1-1-12-1222-1-1-1-1-1-1-1-2-2-1-1-1-1-2-2-2-2111111111111020200-2-200-1-100-1-100001111000000
χ1222222222-12222-122-1-1-12-12-1-1-1-12-1222-1-1-1-1-1-1-1-2-2-1-1-1-1-2-2-2-21111111111110-20-20022001100110000-1-1-1-1000000
χ132222222-12222-12-1-122-1-12-12-1-1-1-12-1-1-1222-1-1-1-122-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-120202200-1-100-1-100-1-1-1-10000000000
χ142222222-12222-12-1-122-1-12-12-1-1-1-12-1-1-1222-1-1-1-122-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-20-20-2-2001100110011110000000000
χ152222222-12222-12-1-122-1-12-12-1-1-1-12-1-1-1222-1-1-1-1-2-2-1-1-1-11111-2-2-2-2111111112020-2-200-1-100-1-10011110000000000
χ162222222-12222-12-1-122-1-12-12-1-1-1-12-1-1-1222-1-1-1-1-2-2-1-1-1-11111-2-2-2-211111111-20-20220011001100-1-1-1-10000000000
χ1722222-2-222-2-222222222-2-222222-2-22-2-22-2-2222200-2-2-2-2000000000000000000000000000000000000000000002-2
χ1822222-2-222-2-222222222-2-222222-2-22-2-22-2-2222200-2-2-2-200000000000000000000000000000000000000000000-22
χ192222-22-2222-2-222222222-2-2-22-2-2-22-22-2-22-222-2-2002-22-2000000000000000000002i−2i00000000002i2i−2i−2i0000000000
χ202222-22-2222-2-222222222-2-2-22-2-2-22-22-2-22-222-2-2002-22-200000000000000000000−2i2i0000000000−2i−2i2i2i0000000000
χ212222-22-2-122-2-2-12-1-122-1-1-21-2-111121-11-22-2-1-11100-11-1133−3−300003333−3−3−3−300002i−2i00−i3i300−i3i300−i−iii0000000000
χ222222-22-2-122-2-2-12-1-122-1-1-21-2-111121-11-22-2-1-11100-11-1133−3−300003333−3−3−3−30000−2i2i00i3−i300i3−i300ii−i−i0000000000
χ232222-22-2-122-2-2-12-1-122-1-1-21-2-111121-11-22-2-1-11100-11-11−3−3330000−3−3−3−3333300002i−2i00i3−i300i3−i300−i−iii0000000000
χ242222-22-2-122-2-2-12-1-122-1-1-21-2-111121-11-22-2-1-11100-11-11−3−3330000−3−3−3−333330000−2i2i00−i3i300−i3i300ii−i−i0000000000
χ252222-2-2222-22-22222222-22-2-22-2-22-2-2-22-2-2222-2-200-22-2200000000000000000000002i−2i0000000000002i2i−2i−2i000000
χ262222-2-2222-22-22222222-22-2-22-2-22-2-2-22-2-2222-2-200-22-220000000000000000000000−2i2i000000000000−2i−2i2i2i000000
χ272222-2-222-1-22-22-122-1-1-1-2-1-21-11121-2-2211-1-1-111001-11-1000033−3−333−3−333−3−30000002i−2i00−i3i300−i3i30000−i−iii000000
χ282222-2-222-1-22-22-122-1-1-1-2-1-21-11121-2-2211-1-1-111001-11-1000033−3−333−3−333−3−3000000−2i2i00i3−i300i3−i30000ii−i−i000000
χ292222-2-222-1-22-22-122-1-1-1-2-1-21-11121-2-2211-1-1-111001-11-10000−3−333−3−333−3−3330000002i−2i00i3−i300i3−i30000−i−iii000000
χ302222-2-222-1-22-22-122-1-1-1-2-1-21-11121-2-2211-1-1-111001-11-10000−3−333−3−333−3−333000000−2i2i00−i3i300−i3i30000ii−i−i000000
χ3122-2-222222-2-2-222-2-2-2-22222222222-2-2-2-2-2-2-2-2-2-22-222-2-22-22-22-22-22-22-22-22-2000000000000000000000000000000
χ3222-2-222222-2-2-222-2-2-2-22222222222-2-2-2-2-2-2-2-2-2-2-2222-2-2-22-22-22-22-22-22-22-22000000000000000000000000000000
χ3322-2-22222-1-2-2-22-1-2-211-12-12-1-1-1-12-1-2-2-211111112-2-1-1112-22-2-11-11-11-11-11-110000000000−i3i300i3−i30000−i3i3−i3i3000000
χ3422-2-22222-1-2-2-22-1-2-211-12-12-1-1-1-12-1-2-2-211111112-2-1-1112-22-2-11-11-11-11-11-110000000000i3−i300−i3i30000i3−i3i3−i3000000
χ3522-2-22222-1-2-2-22-1-2-211-12-12-1-1-1-12-1-2-2-21111111-22-1-111-22-221-11-11-11-11-11-10000000000−i3i300i3−i30000i3−i3i3−i3000000
χ3622-2-22222-1-2-2-22-1-2-211-12-12-1-1-1-12-1-2-2-21111111-22-1-111-22-221-11-11-11-11-11-10000000000i3−i300−i3i30000−i3i3−i3i3000000
χ3722-2-2222-12-2-2-2-1211-2-2-1-12-12-1-1-1-12111-2-2-211112-2-1-111-11-112-22-2-11-11-11-1100000000−i3i300i3−i300−i3i3−i3i30000000000
χ3822-2-2222-12-2-2-2-1211-2-2-1-12-12-1-1-1-12111-2-2-211112-2-1-111-11-112-22-2-11-11-11-1100000000i3−i300−i3i300i3−i3i3−i30000000000
χ3922-2-2222-12-2-2-2-1211-2-2-1-12-12-1-1-1-12111-2-2-21111-22-1-1111-11-1-22-221-11-11-11-100000000−i3i300i3−i300i3−i3i3−i30000000000
χ4022-2-2222-12-2-2-2-1211-2-2-1-12-12-1-1-1-12111-2-2-21111-22-1-1111-11-1-22-221-11-11-11-100000000i3−i300−i3i300−i3i3−i3i30000000000
χ4122-2-22-2-22222-222-2-2-2-22-2-222222-2-2-222-222-2-2-2-200-2-22200000000000000000000000000000000000000002i2i−2i−2i00
χ4222-2-22-2-22222-222-2-2-2-22-2-222222-2-2-222-222-2-2-2-200-2-2220000000000000000000000000000000000000000−2i−2i2i2i00
χ4322-2-2-22-222-22222-2-2-2-222-2-2-22-2-2-222-222-22-2-222002-2-22000000000000000020-2000002200-2-20000000000000000
χ4422-2-2-22-222-22222-2-2-2-222-2-2-22-2-2-222-222-22-2-222002-2-220000000000000000-20200000-2-200220000000000000000
χ4522-2-2-22-2-12-222-1211-2-2-1-1-21-2-11112-11-12-2211-1-100-111-13−3−3300003−33−3−33−3320-200000-1-10011003−3−330000000000
χ4622-2-2-22-2-12-222-1211-2-2-1-1-21-2-11112-11-12-2211-1-100-111-13−3−3300003−33−3−33−33-202000001100-1-100−333−30000000000
χ4722-2-2-22-2-12-222-1211-2-2-1-1-21-2-11112-11-12-2211-1-100-111-1−333−30000−33−333−33−320-200000-1-1001100−333−30000000000
χ4822-2-2-22-2-12-222-1211-2-2-1-1-21-2-11112-11-12-2211-1-100-111-1−333−30000−33−333−33−3-202000001100-1-1003−3−330000000000
χ4922-2-2-2-22222-2222-2-2-2-22-22-2-22-2-22-222-222-2-2-22200-222-20000000000000000020-20000002200-2-200000000000000
χ5022-2-2-2-22222-2222-2-2-2-22-22-2-22-2-22-222-222-2-2-22200-222-200000000000000000-202000000-2-2002200000000000000
χ5122-2-2-2-222-12-222-1-2-211-1-2-1-21-1112122-2-1-1111-1-1001-1-1100003−3−333−3−333−3−33020-2000000-1-1001100003−3−33000000
χ5222-2-2-2-222-12-222-1-2-211-1-2-1-21-1112122-2-1-1111-1-1001-1-1100003−3−333−3−333−3−330-2020000001100-1-10000−333−3000000
χ5322-2-2-2-222-12-222-1-2-211-1-2-1-21-1112122-2-1-1111-1-1001-1-110000−333−3−333−3−333−3020-2000000-1-100110000−333−3000000
χ5422-2-2-2-222-12-222-1-2-211-1-2-1-21-1112122-2-1-1111-1-1001-1-110000−333−3−333−3−333−30-2020000001100-1-100003−3−33000000
χ554444444-2-2444-2-2-2-2-2-21-2-2-2-2111-2-2-2-2-2-2-2-21111441111-2-2-2-2-2-2-2-211111111000000000000000000000000000000
χ564444444-2-2444-2-2-2-2-2-21-2-2-2-2111-2-2-2-2-2-2-2-21111-4-4111122222222-1-1-1-1-1-1-1-1000000000000000000000000000000
χ5744444-4-44-2-4-444-244-2-2-2-424-2-2-2-2-424-4-4-222-2-2-2-20022220000000000000000000000000000000000000000000000
χ5844444-4-4-24-4-44-24-2-244-22-4-24-2-2-22-4-2224-4-4-2-2-2-20022220000000000000000000000000000000000000000000000
χ5944444-4-4-2-2-4-44-2-2-2-2-2-2122-2-211122-222-222111100-1-1-1-10000000033-3-3-3-333000000000000000000000000000000
χ6044444-4-4-2-2-4-44-2-2-2-2-2-2122-2-211122-222-222111100-1-1-1-100000000-3-33333-3-3000000000000000000000000000000
χ614444-44-44-24-4-44-244-2-2-242-42-222-4-2-44-42-22-2-22200-22-220000000000000000000000000000000000000000000000
χ624444-44-4-2-24-4-4-2-2-2-2-2-21-22221-1-12-22-222-2211-1-1001-11-12323−23−230000−3−3−3−33333000000000000000000000000000000
χ634444-44-4-2-24-4-4-2-2-2-2-2-21-22221-1-12-22-222-2211-1-1001-11-1−23−23232300003333−3−3−3−3000000000000000000000000000000
χ644444-4-44-24-44-4-24-2-244-2242-4-222-2-422-2-4-44-2-222002-22-20000000000000000000000000000000000000000000000
χ654444-4-44-2-2-44-4-2-2-2-2-2-212-2221-1-1-2222-222-211-1-100-11-1100002323−23−23−3−333−3−333000000000000000000000000000000
χ664444-4-44-2-2-44-4-2-2-2-2-2-212-2221-1-1-2222-222-211-1-100-11-110000−23−23232333−3−333−3−3000000000000000000000000000000
χ6744-4-4444-2-2-4-4-4-2-222221-2-2-2-2111-2-2222222-1-1-1-14-411-1-1-22-22-22-221-11-11-11-1000000000000000000000000000000
χ6844-4-4444-2-2-4-4-4-2-222221-2-2-2-2111-2-2222222-1-1-1-1-4411-1-12-22-22-22-2-11-11-11-11000000000000000000000000000000
χ6944-4-44-4-44-244-44-2-4-422-2-424-2-2-2-2-42-4442-2-222220022-2-20000000000000000000000000000000000000000000000
χ7044-4-44-4-4-2444-4-2422-4-4-22-4-24-2-2-22-42-2-2-44422220022-2-20000000000000000000000000000000000000000000000
χ7144-4-44-4-4-2-244-4-2-22222122-2-2111222-2-22-2-2-1-1-1-100-1-111000000003-3-33-333-3000000000000000000000000000000
χ7244-4-44-4-4-2-244-4-2-22222122-2-2111222-2-22-2-2-1-1-1-100-1-11100000000-333-33-3-33000000000000000000000000000000
χ7344-4-4-44-44-2-4444-2-4-422-242-42-222-4-24-44-22-222-2-200-222-20000000000000000000000000000000000000000000000
χ7444-4-4-44-4-2-2-444-2-222221-22221-1-12-2-22-2-22-2-1-111001-1-1123−23−23230000−33−333−33−3000000000000000000000000000000
χ7544-4-4-44-4-2-2-444-2-222221-22221-1-12-2-22-2-22-2-1-111001-1-11−232323−2300003−33−3−33−33000000000000000000000000000000
χ7644-4-4-4-44-244-44-2422-4-4-2242-4-222-2-4-2-2244-422-2-2002-2-220000000000000000000000000000000000000000000000
χ7744-4-4-4-44-2-24-44-2-2222212-2221-1-1-22-2-22-2-22-1-11100-111-1000023−23−2323−333−3−333−3000000000000000000000000000000
χ7844-4-4-4-44-2-24-44-2-2222212-2221-1-1-22-2-22-2-22-1-11100-111-10000−232323−233−3−333−3−33000000000000000000000000000000
χ794-44i−4i00044000-4-44i−4i4i−4i40000-400000000004i−4i0000000000000000000000000000000000000000000000002ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ1300
χ804-44i−4i00044000-4-44i−4i4i−4i40000-400000000004i−4i000000000000000000000000000000000000000000000000−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ1300
χ814-4−4i4i00044000-4-4−4i4i−4i4i40000-40000000000−4i4i000000000000000000000000000000000000000000000000−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ2300
χ824-4−4i4i00044000-4-4−4i4i−4i4i40000-40000000000−4i4i0000000000000000000000000000000000000000000000002ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ2300
χ838-88i−8i0008-4000-848i−8i−4i4i-4000040000000000−4i4i000000000000000000000000000000000000000000000000000000
χ848-88i−8i000-480004-8−4i4i8i−8i-4000040000000000−4i4i000000000000000000000000000000000000000000000000000000
χ858-88i−8i000-4-400044−4i4i−4i4i20000-26-6000000002i−2i6i−6i0000000000000000000000000000000000000000000000000000
χ868-88i−8i000-4-400044−4i4i−4i4i20000-2-66000000002i−2i−6i6i0000000000000000000000000000000000000000000000000000
χ878-8−8i8i0008-4000-84−8i8i4i−4i-40000400000000004i−4i000000000000000000000000000000000000000000000000000000
χ888-8−8i8i000-480004-84i−4i−8i8i-40000400000000004i−4i000000000000000000000000000000000000000000000000000000
χ898-8−8i8i000-4-4000444i−4i4i−4i20000-26-600000000−2i2i−6i6i0000000000000000000000000000000000000000000000000000
χ908-8−8i8i000-4-4000444i−4i4i−4i20000-2-6600000000−2i2i6i−6i0000000000000000000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 24 (ζ24 = 1); i = ζ6.