Finite Group Databasebeta

← Group #10693714

Character table — Group #10693714

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90
size1111111122222222222222224444444444444444444444444444444444444416161616161616161616161624242424242424242424242424242424
order122244442234444446661212121244668888888812121212121212121212242424242424242424242424242424242466881212242424244444888888888888
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111
χ411111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1
χ51111111111111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-1-1-1-111111111-1-1-1-1-1-1-1-1
χ61111111111111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-1-1-1-1-1-1-1-1-1-1-1-111111111
χ71111111111111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111111111-1-1-1-11111-1-1-1-1
χ81111111111111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-11111-1-1-1-11111
χ91111-1-1-1-1-1-111-1-1111111-1-1-1-11-1-1-1iiii−i−i−i−i1111-1-111-1-1iiiiiiii−i−i−i−i−i−i−i−i1-111i−i-1-1ii−i−iii−i−ii−ii−i11-1-111-1-1
χ101111-1-1-1-1-1-111-1-1111111-1-1-1-11-1-1-1iiii−i−i−i−i1111-1-111-1-1iiiiiiii−i−i−i−i−i−i−i−i1-111i−i-1-1ii−i−i−i−iii−ii−ii-1-111-1-111
χ111111-1-1-1-1-1-111-1-1111111-1-1-1-11-1-1-1iiii−i−i−i−i1111-1-111-1-1iiiiiiii−i−i−i−i−i−i−i−i-11-1-1−ii11−i−iiiii−i−i−ii−ii-1-11111-1-1
χ121111-1-1-1-1-1-111-1-1111111-1-1-1-11-1-1-1iiii−i−i−i−i1111-1-111-1-1iiiiiiii−i−i−i−i−i−i−i−i-11-1-1−ii11−i−iii−i−iiii−ii−i11-1-1-1-111
χ131111-1-1-1-1-1-111-1-1111111-1-1-1-11-1-1-1−i−i−i−iiiii1111-1-111-1-1−i−i−i−i−i−i−i−iiiiiiiii1-111−ii-1-1−i−iiiii−i−ii−ii−i-1-111-1-111
χ141111-1-1-1-1-1-111-1-1111111-1-1-1-11-1-1-1−i−i−i−iiiii1111-1-111-1-1−i−i−i−i−i−i−i−iiiiiiiii1-111−ii-1-1−i−iii−i−iii−ii−ii11-1-111-1-1
χ151111-1-1-1-1-1-111-1-1111111-1-1-1-11-1-1-1−i−i−i−iiiii1111-1-111-1-1−i−i−i−i−i−i−i−iiiiiiiii-11-1-1i−i11ii−i−iii−i−i−ii−ii11-1-1-1-111
χ161111-1-1-1-1-1-111-1-1111111-1-1-1-11-1-1-1−i−i−i−iiiii1111-1-111-1-1−i−i−i−i−i−i−i−iiiiiiiii-11-1-1i−i11ii−i−i−i−iiii−ii−i-1-11111-1-1
χ17222222222222-2-2-2-222222222-2-22200000000-2-2-2-2-2-222-2-20000000000000000000000000000000022-2-200000000
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χ202222222222-1222222-1-1-1-1-1-1-122-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-211-2-21111110000000000000000
χ212222222222-1222222-1-1-1-1-1-1-122-1-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-1-1-1111111111111111122-1-1-2-2-1-111110000000000000000
χ222222222222-1222222-1-1-1-1-1-1-122-1-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-1-1-11111111111111111-2-2112211-1-1-1-10000000000000000
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χ2522222222-2-22-2-2-2-2-2-2222222222-2-200000000-2-22222-2-2-2-20000000000000000000000000000000000002i−2i2i−2i0000
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χ2822222222-2-2-1-22222-2-1-1-1-1-1-1-1-2-21122-2-222-2-2-1-1111111-1-1-1-1-1-11111-1-1-1-1111100i3−i300i3−i3i3−i3i3−i30000000000000000
χ2922222222-2-2-1-22222-2-1-1-1-1-1-1-1-2-211-2-222-2-222-1-1111111-1-11111-1-1-1-11111-1-1-1-100−i3i300−i3i3i3−i3i3−i30000000000000000
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χ422222-2-2-2-2-2-2-12-2-2222-1-1-111112-2112i2i2i2i−2i−2i−2i−2i-1-1-1-111-1-111−i−i−i−i−i−i−i−iiiiiiiii-2211−2i2i-1-1ii−i−i0000000000000000
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χ754-44-4−4i4i4i−4i00-20000002-222i−2i−2i2i00002−2i−2+2i002+2i−2−2i0000−2i32i3−23230000−1+i1−i−1+i1−i−ζ4+ζ14+ζ20−ζ22ζ4−ζ14−ζ20+ζ22−ζ4+ζ14+ζ20−ζ22ζ4−ζ14−ζ20+ζ22−1−i1+i−1−i1+i−ζ4−ζ14+ζ20+ζ22ζ4+ζ14−ζ20−ζ22−ζ4−ζ14+ζ20+ζ22ζ4+ζ14−ζ20−ζ220000000000000000000000000000
χ764-44-4−4i4i4i−4i00-20000002-222i−2i−2i2i00002−2i−2+2i002+2i−2−2i00002i3−2i323−230000−1+i1−i−1+i1−iζ4−ζ14−ζ20+ζ22−ζ4+ζ14+ζ20−ζ22ζ4−ζ14−ζ20+ζ22−ζ4+ζ14+ζ20−ζ22−1−i1+i−1−i1+iζ4+ζ14−ζ20−ζ22−ζ4−ζ14+ζ20+ζ22ζ4+ζ14−ζ20−ζ22−ζ4−ζ14+ζ20+ζ220000000000000000000000000000
χ774-44-4−4i4i4i−4i00-20000002-222i−2i−2i2i0000−2+2i2−2i00−2−2i2+2i0000−2i32i3−232300001−i−1+i1−i−1+iζ4−ζ14−ζ20+ζ22−ζ4+ζ14+ζ20−ζ22ζ4−ζ14−ζ20+ζ22−ζ4+ζ14+ζ20−ζ221+i−1−i1+i−1−iζ4+ζ14−ζ20−ζ22−ζ4−ζ14+ζ20+ζ22ζ4+ζ14−ζ20−ζ22−ζ4−ζ14+ζ20+ζ220000000000000000000000000000
χ784-44-4−4i4i4i−4i00-20000002-222i−2i−2i2i0000−2+2i2−2i00−2−2i2+2i00002i3−2i323−2300001−i−1+i1−i−1+i−ζ4+ζ14+ζ20−ζ22ζ4−ζ14−ζ20+ζ22−ζ4+ζ14+ζ20−ζ22ζ4−ζ14−ζ20+ζ221+i−1−i1+i−1−i−ζ4−ζ14+ζ20+ζ22ζ4+ζ14−ζ20−ζ22−ζ4−ζ14+ζ20+ζ22ζ4+ζ14−ζ20−ζ220000000000000000000000000000
χ794-4-4444-4-44-4440000-4-4-4444-4-4004-4000000000000004-40000000000000000000000000000000000000000000000
χ804-4-4444-4-44-4-240000-422-2-2-22200-2200000000000000-22006−6−666−6−666−6−66−666−60000000000000000000000000000
χ814-4-4444-4-44-4-240000-422-2-2-22200-2200000000000000-2200−666−6−666−6−666−66−6−660000000000000000000000000000
χ824-4-4444-4-4-444-400004-4-4444-4-400-4400000000000000-440000000000000000000000000000000000000000000000
χ834-4-4444-4-4-44-2-40000422-2-2-222002-2000000000000002-2006−6−66−666−66−6−666−6−660000000000000000000000000000
χ844-4-4444-4-4-44-2-40000422-2-2-222002-2000000000000002-200−666−66−6−66−666−6−666−60000000000000000000000000000
χ854-4-44-4-4444-44-400004-4-44-4-444004-400000000000000-440000000000000000000000000000000000000000000000
χ864-4-44-4-4444-4-2-40000422-222-2-200-22000000000000002-200i6−i6−i6i6−i6i6i6−i6−i6i6i6−i6−i6i6i6−i60000000000000000000000000000
χ874-4-44-4-4444-4-2-40000422-222-2-200-22000000000000002-200−i6i6i6−i6i6−i6−i6i6i6−i6−i6i6i6−i6−i6i60000000000000000000000000000
χ884-4-44-4-444-44440000-4-4-44-4-44400-44000000000000004-40000000000000000000000000000000000000000000000
χ894-4-44-4-444-44-240000-422-222-2-2002-200000000000000-2200i6−i6−i6i6i6−i6−i6i6−i6i6i6−i6i6−i6−i6i60000000000000000000000000000
χ904-4-44-4-444-44-240000-422-222-2-2002-200000000000000-2200−i6i6i6−i6−i6i6i6−i6i6−i6−i6i6−i6i6i6−i60000000000000000000000000000

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