Finite Group Databasebeta

← Group #13156596

Character table — Group #13156596

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108
size1111222222222222224444444444444444444444666688888888888812121212121212121212121212121212181818182424242424242424242424242424242424243636363654545454727272727272
order1222333446666666663336666666661212121212121212121288883666121212121212121224242424242424242424242424242424888844121212121212121212121212121212122424242444444412121212
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-11-111-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-11-111-1-1
χ4111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-11-1-111-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-11-1-111
χ51111111111111111111111111111111111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111111111111111-1-1-1-1-1-1-1-1-1-1
χ61111111111111111111111111111111111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111111
χ71111111111111111111111111111111111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-111-1-111-1-11111-1-1-1-1-1-1-1-11111-11-1-111
χ81111111111111111111111111111111111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-111-1-111-1-1-1-11111-1-1-1-111111-111-1-1
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χ13222222-1222222-1-122-12-1-122-1-1-1-1-12-122-1-1-12-1-1-12-2-2-2-2-1-1-1-122-1-1-1-1-1-1-2-2-2-2111111111111000002002200-1-10000-1-1-1-1000000000-20011
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χ854-4-444-2-24-4-4-422224-2-2-2-212222-1-11-2-2422-1-1-2-211-4-444-41-1-11-22-2211-1-12-2-222-2-22-1-11111-1-1000000000000000000000000000000000000
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χ874-4-444-2-2-44-4-422224-2-2-2-212222-1-11-2-2-4-2-21122-1-1400001-1-112-22-2-1-11100000000−3i3i3i−3i3i−3i−3i3i000000000000000000000000000000000000
χ884-4-44-2444-422-4-4-4-4-244-2-242222-4-44-2-2-2-4-4-4-4444420000-222-2-22-22-2-2220000000000000000000000000000000000000000000000000000
χ894-4-44-24-24-422-4-422-24-2-21-222-1-122-2-21-2-42224-2-2-2200001-1-11-221-111-1-10000000000000000000000000000−2i32i30000i3i3−i3−i300000000000000
χ904-4-44-24-24-422-4-422-24-2-21-222-1-122-2-21-2-42224-2-2-2200001-1-11-221-111-1-100000000000000000000000000002i3−2i30000−i3−i3i3i300000000000000
χ914-4-44-24-2-4422-4-422-24-2-21-222-1-122-2-2124-2-2-2-4222-200001-1-112-2-11-1-111000000000000000000000000−2i32i300000000i3−i3i3−i300000000000000
χ924-4-44-24-2-4422-4-422-24-2-21-222-1-122-2-2124-2-2-2-4222-200001-1-112-2-11-1-1110000000000000000000000002i3−2i300000000−i3i3−i3i300000000000000
χ934-4-44-2-244-42222-4-4-2-241-2-2-1-12222-21-2-22-422-24-2-2200001-1-111-1-2211-1-100000000000000000000000000−2i32i300i3i3−i3−i3000000000000000000
χ944-4-44-2-244-42222-4-4-2-241-2-2-1-12222-21-2-22-422-24-2-2200001-1-111-1-2211-1-1000000000000000000000000002i3−2i300−i3−i3i3i3000000000000000000
χ954-4-44-2-24-442222-4-4-2-241-2-2-1-12222-21-22-24-2-22-422-200001-1-11-112-2-1-1110000000000000000000000−2i32i3000000i3−i3i3−i3000000000000000000
χ964-4-44-2-24-442222-4-4-2-241-2-2-1-12222-21-22-24-2-22-422-200001-1-11-112-2-1-11100000000000000000000002i3−2i3000000−i3i3−i3i3000000000000000000
χ978888-4-4-488-4-4-4-4-4-4-4-4-4222222222222-4-4-422-4-422-40000-1-1-1-12222-1-1-1-10000000000000000000000000000000000000000000000000000
χ988888-4-4-4-8-8-4-4-4-4-4-4-4-4-4222222222222444-2-244-2-240000-1-1-1-1-2-2-2-211110000000000000000000000000000000000000000000000000000
χ9988-8-8-48-400-448-8-444-84-42-4-442-2-4444-20000000000000022-2-2000000000000000000000000000000000000000000000000000000000000
χ10088-8-8-4-4800-44-448-844-82-4-42-2-44-444-240000000000000022-2-2000000000000000000000000000000000000000000000000000000000000
χ10188-8-8-4-4-400-44-44-444442222-22-22-2-2-2-20006i−6i006i−6i00000-1-1110000−3i3i−3i3i0000000000000000000000000000000000000000000000000000
χ10288-8-8-4-4-400-44-44-444442222-22-22-2-2-2-2000−6i6i00−6i6i00000-1-11100003i−3i3i−3i0000000000000000000000000000000000000000000000000000
χ1038-88-8-48-4004-4-884-44-84-42-44-4-224-444-2000000000000002-22-2000000000000000000000000000000000000000000000000000000000000
χ1048-88-8-4-48004-44-4-8844-82-4-4-224-44-44-24000000000000002-22-2000000000000000000000000000000000000000000000000000000000000
χ1058-88-8-4-4-4004-44-44-4444222-22-22-22-2-2-20006i−6i00−6i6i00000-11-1100003i−3i−3i3i0000000000000000000000000000000000000000000000000000
χ1068-88-8-4-4-4004-44-44-4444222-22-22-22-2-2-2000−6i6i006i−6i00000-11-110000−3i3i3i−3i0000000000000000000000000000000000000000000000000000
χ1078-8-88-4-4-48-8444444-4-4-4222-2-2-2-2-2-2222-444-2-2-4-42240000-111-12-22-2-1-1110000000000000000000000000000000000000000000000000000
χ1088-8-88-4-4-4-88444444-4-4-4222-2-2-2-2-2-22224-4-42244-2-2-40000-111-1-22-2211-1-10000000000000000000000000000000000000000000000000000

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