Finite Group Databasebeta

← Group #13161323

Character table — Group #13161323

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114
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order1223333344666666633334466666666666666661212121212121212121212121212121212121212121212121212121212121212121212121212121212121212882424242424242424242424242424242444121212122662244
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111-1-1-1-1
χ411111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ5111111111111111111111-1-111111111111111111111111111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-111111111-1-1-1-1-1-1-1-1111111-1-1-11-11-1
χ6111111111111111111111-1-111111111111111111111111111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111-11-11
χ7111111111111111111111-1-111111111111111111111111111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-111111111111111-1-1-1-11-11
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χ112222222-1222222-1-1-1-1-1-1-1222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1222222222222-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-100000000000000000022-1-1-1-12-1-10000
χ122222222-1222222-1-1-1-1-1-1-1222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1222222222222-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000000000000000000-2-21111-2110000
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χ41222-1-12-12-2-2-1-12-1222-1-12-1-22-1-12-1-1-1-1-122-1-1-1-12-1-2-21111-2-21111-21-2-1-12-121111-2-2111111-2-211-1-1-1-122-1-1003−3−3033−30−3330−3−3300000000000000
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χ5122-2222222-222222-2-2222200-2-2-2-2-2-2-2-2-2-2-2-222222-22-22-22-22-200000000002-22-22-22-20000000000000000000000000000000000000000000020-2
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χ7644-44-2-2-2-24-44-2-2-2-222-211100-422222-1-1-1-1-1-1-2111-224-4-22-22-220000000000-221-11-11-100-33-33-3300-33-33-330000000000000000000000000000000
χ7744-44-2-2-2-2-444-2-2-2-222-211100-422222-1-1-1-1-1-1-21112-2-442-22-22-200000000002-2-11-11-11003-33-33-300-33-33-330000000000000000000000000000000
χ7844-44-2-2-2-2-444-2-2-2-222-211100-422222-1-1-1-1-1-1-21112-2-442-22-22-200000000002-2-11-11-1100-33-33-33003-33-33-30000000000000000000000000000000
χ7944-4-24-2-244-4-24-2-24-4-4-24-2-2002-42222-4-42222-24-2-24-4-224-4-22-220000000000-224-4-22-2200000000000000000000000000000000000000000000000
χ8044-4-24-2-24-44-24-2-24-4-4-24-2-2002-42222-4-42222-24-2-2-442-2-442-22-200000000002-2-442-22-200000000000000000000000000000000000000000000000
χ8144-4-24-2-2-24-4-24-2-2-2221-211002-422-1-122-1-1-1-11-211-22-224-4-22-2200000000001-1-221-11-13-3003-3-333-3003-3-330000000000000000000000000000000
χ8244-4-24-2-2-24-4-24-2-2-2221-211002-422-1-122-1-1-1-11-211-22-224-4-22-2200000000001-1-221-11-1-3300-333-3-3300-333-30000000000000000000000000000000
χ8344-4-24-2-2-2-44-24-2-2-2221-211002-422-1-122-1-1-1-11-2112-22-2-442-22-20000000000-112-2-11-113-3003-3-33-3300-333-30000000000000000000000000000000
χ8444-4-24-2-2-2-44-24-2-2-2221-211002-422-1-122-1-1-1-11-2112-22-2-442-22-20000000000-112-2-11-11-3300-333-33-3003-3-330000000000000000000000000000000
χ8544-4-2-24-244-4-2-24-24-4-4-2-24-20022-422222-4-422-2-24-24-4-22-224-4-220000000000-22-224-4-2200000000000000000000000000000000000000000000000
χ8644-4-2-24-24-44-2-24-24-4-4-2-24-20022-422222-4-422-2-24-2-442-22-2-442-200000000002-22-2-442-200000000000000000000000000000000000000000000000
χ8744-4-2-24-2-24-4-2-24-2-22211-210022-42-1-1-1-122-1-111-21-22-22-224-4-2200000000001-11-1-221-13-3-33003-33-3-33003-30000000000000000000000000000000
χ8844-4-2-24-2-24-4-2-24-2-22211-210022-42-1-1-1-122-1-111-21-22-22-224-4-2200000000001-11-1-221-1-333-300-33-333-300-330000000000000000000000000000000
χ8944-4-2-24-2-2-44-2-24-2-22211-210022-42-1-1-1-122-1-111-212-22-22-2-442-20000000000-11-112-2-113-3-33003-3-333-300-330000000000000000000000000000000
χ9044-4-2-24-2-2-44-2-24-2-22211-210022-42-1-1-1-122-1-111-212-22-22-2-442-20000000000-11-112-2-11-333-300-333-3-33003-30000000000000000000000000000000
χ9144-4-2-2-2444-4-2-2-244-4-4-2-2-2400222-4222222-4-4-2-2-244-4-22-22-224-40000000000-22-22-224-400000000000000000000000000000000000000000000000
χ9244-4-2-2-244-44-2-2-244-4-4-2-2-2400222-4222222-4-4-2-2-24-442-22-22-2-4400000000002-22-22-2-4400000000000000000000000000000000000000000000000
χ9344-4-2-2-24-24-4-2-2-24-222111-200222-4-1-1-1-1-1-122111-2-22-22-22-224-400000000001-11-11-1-223-33-3-33003-33-3-33000000000000000000000000000000000
χ9444-4-2-2-24-24-4-2-2-24-222111-200222-4-1-1-1-1-1-122111-2-22-22-22-224-400000000001-11-11-1-22-33-333-300-33-333-3000000000000000000000000000000000
χ9544-4-2-2-24-2-44-2-2-24-222111-200222-4-1-1-1-1-1-122111-22-22-22-22-2-440000000000-11-11-112-23-33-3-3300-33-333-3000000000000000000000000000000000
χ9644-4-2-2-24-2-44-2-2-24-222111-200222-4-1-1-1-1-1-122111-22-22-22-22-2-440000000000-11-11-112-2-33-333-3003-33-3-33000000000000000000000000000000000
χ974-404444400-4-4-4-4-400444400000000000000-4-4-4-4000000000000000000000000000000000000000000000000000000000000002i−2i2i−2i2i−2i0000000
χ984-404444400-4-4-4-4-400444400000000000000-4-4-4-400000000000000000000000000000000000000000000000000000000000000−2i2i−2i2i−2i2i0000000
χ994-404444-200-4-4-4-42−2i32i3-2-2-2-2000000−2i32i3−2i32i3−2i32i3−2i32i32222000000000000000000000000000000000000000000000000000000000000002i−2i2ζ7−2ζ72ζ11−2ζ110000000
χ1004-404444-200-4-4-4-42−2i32i3-2-2-2-2000000−2i32i3−2i32i3−2i32i3−2i32i3222200000000000000000000000000000000000000000000000000000000000000−2i2i−2ζ72ζ7−2ζ112ζ110000000
χ1014-404444-200-4-4-4-422i3−2i3-2-2-2-20000002i3−2i32i3−2i32i3−2i32i3−2i32222000000000000000000000000000000000000000000000000000000000000002i−2i2ζ11−2ζ112ζ7−2ζ70000000
χ1024-404444-200-4-4-4-422i3−2i3-2-2-2-20000002i3−2i32i3−2i32i3−2i32i3−2i3222200000000000000000000000000000000000000000000000000000000000000−2i2i−2ζ112ζ11−2ζ72ζ70000000
χ1038-808-4-4-4800-8444-8008-4-4-400000000000000-8444000000000000000000000000000000000000000000000000000000000000000000000000000
χ1048-808-4-4-4-400-84444−4i34i3-4222000000−4i34i32i3−2i32i3−2i32i3−2i34-2-2-2000000000000000000000000000000000000000000000000000000000000000000000000000
χ1058-808-4-4-4-400-844444i3−4i3-42220000004i3−4i3−2i32i3−2i32i3−2i32i34-2-2-2000000000000000000000000000000000000000000000000000000000000000000000000000
χ1068-80-48-4-48004-844-800-48-4-4000000000000004-844000000000000000000000000000000000000000000000000000000000000000000000000000
χ1078-80-48-4-4-4004-8444−4i34i32-4220000002i3−2i3−4i34i32i3−2i32i3−2i3-24-2-2000000000000000000000000000000000000000000000000000000000000000000000000000
χ1088-80-48-4-4-4004-84444i3−4i32-422000000−2i32i34i3−4i3−2i32i3−2i32i3-24-2-2000000000000000000000000000000000000000000000000000000000000000000000000000
χ1098-80-4-48-480044-84-800-4-48-40000000000000044-84000000000000000000000000000000000000000000000000000000000000000000000000000
χ1108-80-4-48-4-40044-844−4i34i322-420000002i3−2i32i3−2i3−4i34i32i3−2i3-2-24-2000000000000000000000000000000000000000000000000000000000000000000000000000
χ1118-80-4-48-4-40044-8444i3−4i322-42000000−2i32i3−2i32i34i3−4i3−2i32i3-2-24-2000000000000000000000000000000000000000000000000000000000000000000000000000
χ1128-80-4-4-48800444-8-800-4-4-4800000000000000444-8000000000000000000000000000000000000000000000000000000000000000000000000000
χ1138-80-4-4-48-400444-84−4i34i3222-40000002i3−2i32i3−2i32i3−2i3−4i34i3-2-2-24000000000000000000000000000000000000000000000000000000000000000000000000000
χ1148-80-4-4-48-400444-844i3−4i3222-4000000−2i32i3−2i32i3−2i32i34i3−4i3-2-2-24000000000000000000000000000000000000000000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 12 (ζ12 = 1); i = ζ3.