Finite Group Databasebeta

← Group #13156499

Character table — Group #13156499

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105
size111122222222222222444444444444444444444488888888888812121212121212121212121212121212121212122424242424242424242424242424242424363636363636363654547272727272108
order1222333446666666663336666666661212121212121212121236661212121212121212448824242424242424242424242424242424412121212121212121212121212121212448824242424444121212122
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111111111111-111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-111-1
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
χ4111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1111111-1-1-1-111-1-1-1-1-1-111-111-1-11
χ51111111111111111111111111111111111111111111111111111-1-11111111111111111111-1-11111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-111-1-1-1
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
χ71111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-11111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111-1-1111
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
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χ884-4-44-24-2-442-42-2-44-222-21-22-1-122-212-2-2-4-21122-1-141-1-112-22-2-1-1110000000023−2323−23−3−333−3−333000000000000000000000000000000000
χ894-4-44-24-2-442-42-2-44-222-21-22-1-122-212-2-2-4-21122-1-141-1-112-22-2-1-11100000000−2323−232333−3−333−3−3000000000000000000000000000000000
χ904-4-44-2-244-422-4-22-24-421-2-2-122221-2-1-22-2-422-24-2-221-1-111-1-2211-1-14i−4i0000000000000000000−2i2i0000−2i2iii−i−i00000000000000000000
χ914-4-44-2-244-422-4-22-24-421-2-2-122221-2-1-22-2-422-24-2-221-1-111-1-2211-1-1−4i4i00000000000000000002i−2i00002i−2i−i−iii00000000000000000000
χ924-4-44-2-24-4422-4-22-24-421-2-2-122221-2-1-2-224-2-22-422-21-1-11-112-2-1-111000000000000000000000000000003i−3i−3i3i00000000000000000000
χ934-4-44-2-24-4422-4-22-24-421-2-2-122221-2-1-2-224-2-22-422-21-1-11-112-2-1-11100000000000000000000000000000−3i3i3i−3i00000000000000000000
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
χ9688-8-88-4-4008-44-8444-4-8-4-42-44-4-22444-200000000002-22-20000000000000000000000000000000000000000000000000000000000000
χ9788-8-8-4-4800-4-4-8444-8842-4-424-44-4-24-2400000000002-22-20000000000000000000000000000000000000000000000000000000000000
χ9888-8-8-4-4-400-4-444444-442222-22-22-2-2-2-20006i−6i006i−6i0-11-110000−3i3i−3i3i00000000000000000000000000000000000000000000000000000
χ9988-8-8-4-4-400-4-444444-442222-22-22-2-2-2-2000−6i6i00−6i6i0-11-1100003i−3i3i−3i00000000000000000000000000000000000000000000000000000
χ1008-88-88-4-400-84-4-8-44448-4-424-442-244-4-2000000000022-2-20000000000000000000000000000000000000000000000000000000000000
χ1018-88-8-4-48004484-44-8-8-42-4-4-2-44-44-2424000000000022-2-20000000000000000000000000000000000000000000000000000000000000
χ1028-88-8-4-4-40044-44-4444-4222-22-22-2-2-22-20006i−6i00−6i6i0-1-11100003i−3i−3i3i00000000000000000000000000000000000000000000000000000
χ1038-88-8-4-4-40044-44-4444-4222-22-22-2-2-22-2000−6i6i006i−6i0-1-1110000−3i3i3i−3i00000000000000000000000000000000000000000000000000000
χ1048-8-88-4-4-48-8444-44-4-444222-2-2-2-2-222-224-44-2-2-4-4224-111-12-22-2-1-11100000000000000000000000000000000000000000000000000000
χ1058-8-88-4-4-4-88444-44-4-444222-2-2-2-2-222-22-44-42244-2-2-4-111-1-22-2211-1-100000000000000000000000000000000000000000000000000000

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