Finite Group Databasebeta

← Group #13156444

Character table — Group #13156444

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105
size111122222222222222444444444444444444444488888888888812121212121212121212121212121212121212122424242424242424242424242424242424363636363636363654547272727272108
order12223334466666666633366666666612121212121212121212366612121212121212124488242424242424242424242424242424244121212121212121212121212121212124488242424244426612122
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111111111111-111-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111-1-1-1
χ3111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111111-1-1111111-1-1-1-1-1-1-1-1
χ4111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-11111-1-1-1-111-1-1-1-1-1-111-1-1-1111
χ51111111111111111111111111111111111111111111111111111-1-11111111111111111111-1-111-1-111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-111-1
χ61111111111111111111111111111111111111111111111111111-1-1111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-11
χ71111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-111-1-111-1-1-1-11111-1-1-1-1-1-1-1-111111-1-11
χ81111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111111-1
χ92222222-2-2222222222222222222222-2-2-2-2-2-2-2-2-2-22222-2-2-2-2-2-2-2-20000000000000000000000000000000000000000000002200000-2
χ102222222-2-2222222222222222222222-2-2-2-2-2-2-2-2-2-22222-2-2-2-2-2-2-2-2000000000000000000000000000000000000000000000-2-2000002
χ11222222-1222-122-12-1222-1-12-1-1-12-1-12-122-1-1-12-1-1-12-1-1-1-122-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-10-1-1002200-1-1-1-1000000000000002-1-1000
χ12222222-1222-122-12-1222-1-12-1-1-12-1-12-122-1-1-12-1-1-12-1-1-1-122-1-1-1-1-1-122-2-2-2-2-2-21111111111110-1-1002200-1-1-1-100000000000000-211000
χ13222222-1222-122-12-1222-1-12-1-1-12-1-12-122-1-1-12-1-1-12-1-1-1-122-1-1-1-1-1-1-2-2222222-1-1-1-1-1-1-1-1-1-1-1-101100-2-200111100000000000000-211000
χ14222222-1222-122-12-1222-1-12-1-1-12-1-12-122-1-1-12-1-1-12-1-1-1-122-1-1-1-1-1-1-2-2-2-2-2-2-2-211111111111101100-2-2001111000000000000002-1-1000
χ1522222-1222222-12-122-1-12-1-12-1-1-12-1-122-12-1-1-12-1-12-1-1-1-1-1-122-1-1-1-10022-1-1-1-12222-1-1-1-1-1-1-1-1200-1-100220000-1-1-1-12200000000000-1-10
χ1622222-1222222-12-122-1-12-1-12-1-1-12-1-122-12-1-1-12-1-12-1-1-1-1-1-122-1-1-1-10022-1-1-1-12222-1-1-1-1-1-1-1-1-2001100-2-200001111-2-200000000000110
χ1722222-1222222-12-122-1-12-1-12-1-1-12-1-122-12-1-1-12-1-12-1-1-1-1-1-122-1-1-1-100-2-21111-2-2-2-211111111200-1-100220000-1-1-1-1-2-200000000000110
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χ292-2-22222-22-2-2222-2-2-2-2222-2-2-2-2222-2-2-22222-2-2-2-222-2-22-22-22-2-2222i−2i00000000000000000002i−2i002i−2i002i2i−2i−2i00000000000000000000
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χ422-2-22-122-221-2-122-2-21-2-1-1211-2-2-1-121112222-2-2-2-2-1-111-11-11-111-1-1−2i2i0000000000000000000−2i2i00i−i−33ii−i−i−33−330000−i3i3−i3i300000000
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χ864-4-44-24-24-422-24-2-422-4-21-22-122-21-22-1-2-42224-2-2-221-1-11-221-111-1-1000000000000000000000000000003i−3i−3i3i00000000000000000000
χ874-4-44-24-24-422-24-2-422-4-21-22-122-21-22-1-2-42224-2-2-221-1-11-221-111-1-100000000000000000000000000000−3i3i3i−3i00000000000000000000
χ884-4-44-24-2-4422-24-2-422-4-21-22-122-21-22-124-2-2-2-4222-21-1-112-2-11-1-1114i−4i0000000000000000000−2i2i00−2i2i00ii−i−i00000000000000000000
χ894-4-44-24-2-4422-24-2-422-4-21-22-122-21-22-124-2-2-2-4222-21-1-112-2-11-1-111−4i4i00000000000000000002i−2i002i−2i00−i−iii00000000000000000000
χ904-4-44-2-244-42-4-2-242-4221-2-2-12221-2-2-12-22-422-24-2-221-1-111-1-2211-1-10000000000000000000000023−2300000000−3−3330000000000000000
χ914-4-44-2-244-42-4-2-242-4221-2-2-12221-2-2-12-22-422-24-2-221-1-111-1-2211-1-100000000000000000000000−23230000000033−3−30000000000000000
χ924-4-44-2-24-442-4-2-242-4221-2-2-12221-2-2-122-24-2-22-422-21-1-11-112-2-1-11100000000000000000000000000023−230000−33−330000000000000000
χ934-4-44-2-24-442-4-2-242-4221-2-2-12221-2-2-122-24-2-22-422-21-1-11-112-2-1-111000000000000000000000000000−232300003−33−30000000000000000
χ948888-4-4-488-4-4-4-4-4-4-4-4-4222222222222-4-4-422-4-422-4-1-1-1-12222-1-1-1-100000000000000000000000000000000000000000000000000000
χ958888-4-4-4-8-8-4-4-4-4-4-4-4-4-4222222222222444-2-244-2-24-1-1-1-1-2-2-2-2111100000000000000000000000000000000000000000000000000000
χ9688-8-8-48-400444-848-4-4-8-42-44-24-44-24-4200000000002-22-20000000000000000000000000000000000000000000000000000000000000
χ9788-8-8-4-48004-844-8-48-442-4-4-244-4-2442-400000000002-22-20000000000000000000000000000000000000000000000000000000000000
χ9888-8-8-4-4-40044444-4-4-44222-2-2-22-2-2-2220006i−6i006i−6i0-11-110000−3i3i−3i3i00000000000000000000000000000000000000000000000000000
χ9988-8-8-4-4-40044444-4-4-44222-2-2-22-2-2-222000−6i6i00−6i6i0-11-1100003i−3i3i−3i00000000000000000000000000000000000000000000000000000
χ1008-88-8-48-400-4-44-84-8448-42-4-42-444-244-2000000000022-2-20000000000000000000000000000000000000000000000000000000000000
χ1018-88-8-4-4800-4844-84-84-42-4-42-4-44-244-24000000000022-2-20000000000000000000000000000000000000000000000000000000000000
χ1028-88-8-4-4-400-4-4444444-4222222-2-2-2-2-2-20006i−6i00−6i6i0-1-11100003i−3i−3i3i00000000000000000000000000000000000000000000000000000
χ1038-88-8-4-4-400-4-4444444-4222222-2-2-2-2-2-2000−6i6i006i−6i0-1-1110000−3i3i3i−3i00000000000000000000000000000000000000000000000000000
χ1048-8-88-4-4-48-844-4-4-44444222-2-2-2-2222-2-2-444-2-2-4-4224-111-12-22-2-1-11100000000000000000000000000000000000000000000000000000
χ1058-8-88-4-4-4-8844-4-4-44444222-2-2-2-2222-2-24-4-42244-2-2-4-111-1-22-2211-1-100000000000000000000000000000000000000000000000000000

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