Finite Group Databasebeta

← Group #13155853

Character table — Group #13155853

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105
size111122222222222222444444444444444444444488888888888812121212121212121212121212121212121212122424242424242424242424242424242424363636363636363654547272727272108
order122233344666666666333666666666121212121212121212123666121212121212121222882424242424242424242424242424242446666666612121212121212122288242424242246612124
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111111111111-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-111-1
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
χ4111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-111-111-1-11
χ51111111111111111111111111111111111111111111111111111-1-11111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-111-1-1-1
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
χ71111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1111-1-1111
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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χ874-4-44-24-24-422-424-2-42-21-2-2-1-12221-2-22422-1-1-2-211-41-1-11-22-2211-1-100002i3−2i32i3−2i30000−i3i3−i3i3−i3i3−i3i3000000000000000000000000000000000
χ884-4-44-24-2-4422-424-2-42-21-2-2-1-12221-2-22-4-2-21122-1-141-1-112-22-2-1-1110000000023−2323−23−3−333−3−333000000000000000000000000000000000
χ894-4-44-24-2-4422-424-2-42-21-2-2-1-12221-2-22-4-2-21122-1-141-1-112-22-2-1-11100000000−2323−232333−3−333−3−3000000000000000000000000000000000
χ904-4-44-2-244-4222-4-242-4-2-2-21222-1-1-2-212-2-42224-2-2-221-1-111-1-2211-1-14-40000000000000000000-22-2211-1-1000000000000000000000000
χ914-4-44-2-244-4222-4-242-4-2-2-21222-1-1-2-212-2-42224-2-2-221-1-111-1-2211-1-1-4400000000000000000002-22-2-1-111000000000000000000000000
χ924-4-44-2-24-44222-4-242-4-2-2-21222-1-1-2-21224-2-2-2-4222-21-1-11-112-2-1-11100000000000000000000000003-3-33000000000000000000000000
χ934-4-44-2-24-44222-4-242-4-2-2-21222-1-1-2-21224-2-2-2-4222-21-1-11-112-2-1-1110000000000000000000000000-333-3000000000000000000000000
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
χ9688-8-88-4-4008-8-4-44444-8-42-4-442-444-24-2000000000022-2-20000000000000000000000000000000000000000000000000000000000000
χ9788-8-8-4-4800-44-484-84-84-4-42-44-42-244-24000000000022-2-20000000000000000000000000000000000000000000000000000000000000
χ9888-8-8-4-4-400-44-4-4444442222-222-2-2-2-2-20006i−6i006i−6i0-1-1110000−3i3i−3i3i00000000000000000000000000000000000000000000000000000
χ9988-8-8-4-4-400-44-4-4444442222-222-2-2-2-2-2000−6i6i00−6i6i0-1-11100003i−3i3i−3i00000000000000000000000000000000000000000000000000000
χ1008-88-88-4-400-884444-4-4-8-42-44-4-24-44-24200000000002-22-20000000000000000000000000000000000000000000000000000000000000
χ1018-88-8-4-48004-44-84-8-484-4-424-44-2244-2-400000000002-22-20000000000000000000000000000000000000000000000000000000000000
χ1028-88-8-4-4-4004-44444-4-44222-22-2-22-2-2-220006i−6i00−6i6i0-11-1100003i−3i−3i3i00000000000000000000000000000000000000000000000000000
χ1038-88-8-4-4-4004-44444-4-44222-22-2-22-2-2-22000−6i6i006i−6i0-11-110000−3i3i3i−3i00000000000000000000000000000000000000000000000000000
χ1048-8-88-4-4-48-84444-4-444-4222-2-2-2-2-2222-2-444-2-2-4-4224-111-12-22-2-1-11100000000000000000000000000000000000000000000000000000
χ1058-8-88-4-4-4-884444-4-444-4222-2-2-2-2-2222-24-4-42244-2-2-4-111-1-22-2211-1-100000000000000000000000000000000000000000000000000000

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