Finite Group Databasebeta

← Group #10693705

Character table — Group #10693705

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96
size111111112222222222222222444444444444444444666666668888888888888888888888121212121212121212121212161616161616242424244848
order122244442234444446661212121244668888888812121212121288888888888812122424242424242424242424242424242488888888888824661212444488
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1
χ4111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ51111111111111111111111111111-1-1-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111-1-1
χ61111111111111111111111111111-1-1-1-1-1-1-1-111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-111
χ71111111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111
χ81111111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111111111-1-1
χ91111-1-1-1-1-1-111111-1-1111-1-1-1-11-1-1-11111-1-1-1-1-1-11111iiii−i−i−i−i11-1-11-11111-1-1-1-11111-1-1-1-1ii−i−iii−i−iii−i−i1-111-1-1ii−i−ii−i
χ101111-1-1-1-1-1-111111-1-1111-1-1-1-11-1-1-11111-1-1-1-1-1-11111iiii−i−i−i−i-1-1111-11111-1-1-1-1-1-1-1-11111ii−i−iii−i−iii−i−i-11-1-111−i−iii−ii
χ111111-1-1-1-1-1-111111-1-1111-1-1-1-11-1-1-11111-1-1-1-1-1-11111−i−i−i−iiiii11-1-11-11111-1-1-1-11111-1-1-1-1−i−iii−i−iii−i−iii1-111-1-1−i−iii−ii
χ121111-1-1-1-1-1-111111-1-1111-1-1-1-11-1-1-11111-1-1-1-1-1-11111−i−i−i−iiiii-1-1111-11111-1-1-1-1-1-1-1-11111−i−iii−i−iii−i−iii-11-1-111ii−i−ii−i
χ131111-1-1-1-1-1-111111-1-1111-1-1-1-11-1-1-1-1-1-1-11111-1-11111iiii−i−i−i−i11-1-11-1-1-1-1-111111111-1-1-1-1−i−iii−i−iiiii−i−i-11-1-111ii−i−i−ii
χ141111-1-1-1-1-1-111111-1-1111-1-1-1-11-1-1-1-1-1-1-11111-1-11111iiii−i−i−i−i-1-1111-1-1-1-1-11111-1-1-1-11111−i−iii−i−iiiii−i−i1-111-1-1−i−iiii−i
χ151111-1-1-1-1-1-111111-1-1111-1-1-1-11-1-1-1-1-1-1-11111-1-11111−i−i−i−iiiii11-1-11-1-1-1-1-111111111-1-1-1-1ii−i−iii−i−i−i−iii-11-1-111−i−iiii−i
χ161111-1-1-1-1-1-111111-1-1111-1-1-1-11-1-1-1-1-1-1-11111-1-11111−i−i−i−iiiii-1-1111-1-1-1-1-11111-1-1-1-11111ii−i−iii−i−i−i−iii1-111-1-1ii−i−i−ii
χ17222222222222-2-22-2-22222222-2-22200000000-2-22-2-22000000000000-2-200000000000000002222-2-2-2-20000000000000000
χ18222222222222-2-22-2-22222222-2-22200000000-2-22-2-22000000000000-2-20000000000000000-2-2-2-222220000000000000000
χ192222222222-1222222-1-1-1-1-1-1-122-1-122222222-1-1-1-1-1-1000000002222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-100000000000022-1-1-1-1000000
χ202222222222-1222222-1-1-1-1-1-1-122-1-122222222-1-1-1-1-1-100000000-2-2-2-2-1-1-1-1-1-1-1-1-1-111111111000000000000-2-21111000000
χ212222222222-1222222-1-1-1-1-1-1-122-1-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1000000002222-1-111111111-1-1-1-1-1-1-1-1000000000000-2-21111000000
χ222222222222-1222222-1-1-1-1-1-1-122-1-1-2-2-2-2-2-2-2-2-1-1-1-1-1-100000000-2-2-2-2-1-1111111111111111100000000000022-1-1-1-1000000
χ2322222222-2-22-222-2222222222-2-2-2-20000000022-222-2222222220000-2-2000000000000000000000000-2-2-2-2000000000000
χ2422222222-2-22-222-2222222222-2-2-2-20000000022-222-2-2-2-2-2-2-2-2-20000-2-20000000000000000000000002222000000000000
χ2522222222-2-22-2-2-2-2-2-2222222222-2-22i2i−2i−2i2i2i−2i−2i-2-2-2-2-2-2000000000000222i2i−2i−2i2i2i−2i−2i00000000000000000000000000000000
χ2622222222-2-22-2-2-2-2-2-2222222222-2-2−2i−2i2i2i−2i−2i2i2i-2-2-2-2-2-200000000000022−2i−2i2i2i−2i−2i2i2i00000000000000000000000000000000
χ2722222222-2-2-1-2-2-2-2-2-2-1-1-1-1-1-1-122112i2i−2i−2i2i2i−2i−2i111111000000000000-1-1−i−iii−i−iii33−3−333−3−300000000000000−i3i3−i3i3000000
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χ3022222222-2-2-1-2-2-2-2-2-2-1-1-1-1-1-1-12211−2i−2i2i2i−2i−2i2i2i111111000000000000-1-1ii−i−iii−i−i−3−333−3−33300000000000000−i3i3−i3i3000000
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χ322222-2-2-2-2222-222-2-2-2222-2-2-2-2-222200000000-2-2-222-2−2i−2i−2i−2i2i2i2i2i0000-220000000000000000000000002i2i−2i−2i000000000000
χ332222-2-2-2-2222-2-2-2-222222-2-2-2-22-2222i2i−2i−2i−2i−2i2i2i22-2-2-2-20000000000002-22i2i−2i−2i−2i−2i2i2i00000000000000000000000000000000
χ342222-2-2-2-2222-2-2-2-222222-2-2-2-22-222−2i−2i2i2i2i2i−2i−2i22-2-2-2-20000000000002-2−2i−2i2i2i2i2i−2i−2i00000000000000000000000000000000
χ352222-2-2-2-222-1-2-2-2-222-1-1-111112-2-1-12i2i−2i−2i−2i−2i2i2i-1-11111000000000000-11−i−iiiii−i−i33−3−3−3−33300000000000000−i3i3i3−i3000000
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χ392222-2-2-2-2-2-222-2-2222222-2-2-2-2-22-2-200000000222-2-22000000000000-2200000000000000002i2i−2i−2i−2i−2i2i2i0000000000000000
χ402222-2-2-2-2-2-222-2-2222222-2-2-2-2-22-2-200000000222-2-22000000000000-220000000000000000−2i−2i2i2i2i2i−2i−2i0000000000000000
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χ422222-2-2-2-2-2-2-12222-2-2-1-1-111112-2112222-2-2-2-211-1-1-1-100000000-2-222-11-1-1-1-111111111-1-1-1-1000000000000-2211-1-1000000
χ432222-2-2-2-2-2-2-12222-2-2-1-1-111112-211-2-2-2-2222211-1-1-1-10000000022-2-2-111111-1-1-1-1-1-1-1-11111000000000000-2211-1-1000000
χ442222-2-2-2-2-2-2-12222-2-2-1-1-111112-211-2-2-2-2222211-1-1-1-100000000-2-222-111111-1-1-1-11111-1-1-1-10000000000002-2-1-111000000
χ4522-2-22i−2i2i−2i00202-202i−2i2-2-22i2i−2i−2i0000000000002i−2i02-202ζ7+2ζ232ζ7+2ζ23−2ζ7−2ζ23−2ζ7−2ζ23−2ζ5−2ζ13−2ζ5−2ζ132ζ5+2ζ132ζ5+2ζ132−2−i2i200000000002−22−2−i2i2−i2i20000000000000000001+i−1−i1−i−1+i00
χ4622-2-22i−2i2i−2i00202-202i−2i2-2-22i2i−2i−2i0000000000002i−2i02-202ζ7+2ζ232ζ7+2ζ23−2ζ7−2ζ23−2ζ7−2ζ23−2ζ5−2ζ13−2ζ5−2ζ132ζ5+2ζ132ζ5+2ζ13−22i2−i20000000000−22−22i2−i2i2−i2000000000000000000−1−i1+i−1+i1−i00
χ4722-2-22i−2i2i−2i00202-202i−2i2-2-22i2i−2i−2i0000000000002i−2i02-20−2ζ7−2ζ23−2ζ7−2ζ232ζ7+2ζ232ζ7+2ζ232ζ5+2ζ132ζ5+2ζ13−2ζ5−2ζ13−2ζ5−2ζ132−2−i2i200000000002−22−2−i2i2−i2i2000000000000000000−1−i1+i−1+i1−i00
χ4822-2-22i−2i2i−2i00202-202i−2i2-2-22i2i−2i−2i0000000000002i−2i02-20−2ζ7−2ζ23−2ζ7−2ζ232ζ7+2ζ232ζ7+2ζ232ζ5+2ζ132ζ5+2ζ13−2ζ5−2ζ13−2ζ5−2ζ13−22i2−i20000000000−22−22i2−i2i2−i20000000000000000001+i−1−i1−i−1+i00
χ4922-2-2−2i2i−2i2i00202-20−2i2i2-2-2−2i−2i2i2i000000000000−2i2i02-20−2ζ5−2ζ13−2ζ5−2ζ132ζ5+2ζ132ζ5+2ζ132ζ7+2ζ232ζ7+2ζ23−2ζ7−2ζ23−2ζ7−2ζ232−2i2−i200000000002−22−2i2−i2i2−i20000000000000000001−i−1+i1+i−1−i00
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χ5122-2-2−2i2i−2i2i00202-20−2i2i2-2-2−2i−2i2i2i000000000000−2i2i02-202ζ5+2ζ132ζ5+2ζ13−2ζ5−2ζ13−2ζ5−2ζ13−2ζ7−2ζ23−2ζ7−2ζ232ζ7+2ζ232ζ7+2ζ232−2i2−i200000000002−22−2i2−i2i2−i2000000000000000000−1+i1−i−1−i1+i00
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χ532-2-2222-2-22-22-200200-2-222-22-2002-22−22−22−22−200-2002−i2i2−i2i2−i2i2−i2i20000002−22−22−22−20000000000002i−2i2i−2i−i2i2−i2i2000000000000
χ542-2-2222-2-22-22-200200-2-222-22-2002-22−22−22−22−200-2002i2−i2i2−i2i2−i2i2−i20000002−22−22−22−2000000000000−2i2i−2i2ii2−i2i2−i2000000000000
χ552-2-2222-2-22-22-200200-2-222-22-2002-2−22−22−22−2200-2002−i2i2−i2i2−i2i2−i2i2000000−22−22−22−22000000000000−2i2i−2i2i−i2i2−i2i2000000000000
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χ572-2-2222-2-2-222200-200-2-222-22-200-22−i2i2i2−i2−i2i2i2−i200200-2−i2i2−i2i2−i2i2−i2i2000000−i2i2i2−i2−i2i2i2−i2000000002-22-20000i2−i2i2−i2000000000000
χ582-2-2222-2-2-222200-200-2-222-22-200-22−i2i2i2−i2−i2i2i2−i200200-2i2−i2i2−i2i2−i2i2−i2000000−i2i2i2−i2−i2i2i2−i200000000-22-220000−i2i2−i2i2000000000000
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χ602-2-2222-2-2-222200-200-2-222-22-200-22i2−i2−i2i2i2−i2−i2i200200-2i2−i2i2−i2i2−i2i2−i2000000i2−i2−i2i2i2−i2−i2i2000000002-22-20000−i2i2−i2i2000000000000
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χ632-2-22-2-2222-22200-200-2-22-22-22002-2i2−i2−i2i2−i2i2i2−i200200-22−22−2−22−22000000i2−i2−i2i2−i2i2i2−i200000000−2i2i2i−2i0000−222−2000000000000
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χ884-4-4444-4-44-4-2-40040022-2-22-2200-22−2222−2222−2222−222200200-2000000000000002−22−22−22−200000000000000000000000000000000
χ894-4-4444-4-4-44-2400-40022-2-22-22002-2−2i22i22i2−2i2−2i22i22i2−2i200-200200000000000000i2−i2−i2i2i2−i2−i2i200000000000000000000000000000000
χ904-4-4444-4-4-44-2400-40022-2-22-22002-22i2−2i2−2i22i22i2−2i2−2i22i200-200200000000000000−i2i2i2−i2−i2i2i2−i200000000000000000000000000000000
χ914-4-44-4-4444-4-2400-40022-22-22-200-22−2i22i22i2−2i22i2−2i2−2i22i200-200200000000000000i2−i2−i2i2−i2i2i2−i200000000000000000000000000000000
χ924-4-44-4-4444-4-2400-40022-22-22-200-222i2−2i2−2i22i2−2i22i22i2−2i200-200200000000000000−i2i2i2−i2i2−i2−i2i200000000000000000000000000000000
χ934-4-44-4-444-44-2-40040022-22-22-2002-222−2222−22−2222−222200200-200000000000000−22−222−22−200000000000000000000000000000000
χ944-4-44-4-444-44-2-40040022-22-22-2002-2−2222−222222−2222−2200200-2000000000000002−22−2−22−2200000000000000000000000000000000
χ958-88-88i−8i−8i8i00-40000004-44−4i4i4i−4i000000000000000000000000000000000000000000000000000000000000000000000000
χ968-88-8−8i8i8i−8i00-40000004-444i−4i−4i4i000000000000000000000000000000000000000000000000000000000000000000000000

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