Finite Group Databasebeta

← Group #13156416

Character table — Group #13156416

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105
size111122222222222222444444444444444444444488888888888812121212121212121212121212121212121212122424242424242424242424242424242424363636363636363654547272727272108
order12223334466666666633366666666612121212121212121212366612121212121212124488242424242424242424242424242424244121212121212121212121212121212124488242424242226612124
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111111111111-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111-1-1-1
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
χ4111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-111-1-1-1-1-1-111-1-1-1111
χ51111111111111111111111111111111111111111111111111111-1-11111111111111111111-1-1-1-11111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-111-1
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
χ71111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-111111-1-11
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
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χ11222222-122-122-1222-122-1-12-1-1-12-1-12-122-1-1-12-1-1-12-1-1-1-122-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1022-1-10000-1-1-1-1000000000000002-1-1000
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χ13222222-122-122-1222-122-1-12-1-1-12-1-12-122-1-1-12-1-1-12-1-1-1-122-1-1-1-1-1-1-2-2222222-1-1-1-1-1-1-1-1-1-1-1-10-2-2110000111100000000000000-211000
χ14222222-122-122-1222-122-1-12-1-1-12-1-12-122-1-1-12-1-1-12-1-1-1-122-1-1-1-1-1-1-2-2-2-2-2-2-2-21111111111110-2-21100001111000000000000002-1-1000
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χ332-2-2222-1-22122-1-2-2-21-22-1-1-21112-1-1-21-22-1-1-1-21112-111-1-221-111-1-1−2i2i0000003−33−333−3−333−3−30−2i2ii−i0000ii−i−i000000000000000i3−i3000
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χ864-4-44-24-24-42-24-222-42-4-21-22-122-21-22-1-2-42224-2-2-221-1-11-221-111-1-1000000000000000000000000000003i−3i−3i3i00000000000000000000
χ874-4-44-24-24-42-24-222-42-4-21-22-122-21-22-1-2-42224-2-2-221-1-11-221-111-1-100000000000000000000000000000−3i3i3i−3i00000000000000000000
χ884-4-44-24-2-442-24-222-42-4-21-22-122-21-22-124-2-2-2-4222-21-1-112-2-11-1-1114i−4i0000000000000000000−2i2i−2i2i0000ii−i−i00000000000000000000
χ894-4-44-24-2-442-24-222-42-4-21-22-122-21-22-124-2-2-2-4222-21-1-112-2-11-1-111−4i4i00000000000000000002i−2i2i−2i0000−i−iii00000000000000000000
χ904-4-44-2-244-4-4-2-24222-421-2-2-12221-2-2-12-22-422-24-2-221-1-111-1-2211-1-100000000000000000000000000023−230000−3−3330000000000000000
χ914-4-44-2-244-4-4-2-24222-421-2-2-12221-2-2-12-22-422-24-2-221-1-111-1-2211-1-1000000000000000000000000000−2323000033−3−30000000000000000
χ924-4-44-2-24-44-4-2-24222-421-2-2-12221-2-2-122-24-2-22-422-21-1-11-112-2-1-111000000000000000000000000023−23000000−33−330000000000000000
χ934-4-44-2-24-44-4-2-24222-421-2-2-12221-2-2-122-24-2-22-422-21-1-11-112-2-1-1110000000000000000000000000−23230000003−33−30000000000000000
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
χ9688-8-8-48-400-44-84-4484-8-42-442-444-24-4-2000000000022-2-20000000000000000000000000000000000000000000000000000000000000
χ9788-8-8-4-4800844-8-44-4-842-4-4-2-4-44-24424000000000022-2-20000000000000000000000000000000000000000000000000000000000000
χ9888-8-8-4-4-400-4444-44-444222-222-2-2-2-22-20006i−6i006i−6i0-1-1110000−3i3i−3i3i00000000000000000000000000000000000000000000000000000
χ9988-8-8-4-4-400-4444-44-444222-222-2-2-2-22-2000−6i6i00−6i6i0-1-11100003i−3i3i−3i00000000000000000000000000000000000000000000000000000
χ1008-88-8-48-40044-844-4-8-48-42-4-4-24-44-244200000000002-22-20000000000000000000000000000000000000000000000000000000000000
χ1018-88-8-4-4800-844-84-448-42-4-4244-4-244-2-400000000002-22-20000000000000000000000000000000000000000000000000000000000000
χ1028-88-8-4-4-40044444-44-4-42222-2-22-2-2-2-220006i−6i00−6i6i0-11-1100003i−3i−3i3i00000000000000000000000000000000000000000000000000000
χ1038-88-8-4-4-40044444-44-4-42222-2-22-2-2-2-22000−6i6i006i−6i0-11-110000−3i3i3i−3i00000000000000000000000000000000000000000000000000000
χ1048-8-88-4-4-48-84-4-4-444444222-2-2-2-2222-2-2-444-2-2-4-4224-111-12-22-2-1-11100000000000000000000000000000000000000000000000000000
χ1058-8-88-4-4-4-884-4-4-444444222-2-2-2-2222-2-24-4-42244-2-2-4-111-1-22-2211-1-100000000000000000000000000000000000000000000000000000

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