Finite Group Databasebeta

← Group #10694340

Character table — Group #10694340

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96
size111111112222222222222222444444444444444444666666668888888888888888888888121212121212121212121212161616161616242424244848
order12224444223444444666121212124466888888881212121212128888888844441212121212121212121224242424242424248888888888884412121212444444
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
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
χ4111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ51111111111111111111111111111-1-1-1-1-1-1-1-11111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111-1-1
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
χ71111111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111
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
χ91111-1-1-1-1-1-1111-1-111111-1-1-1-11-1-1-1iiii−i−i−i−i1111-1-11111-1-1-1-1ii−i−i1-1iiii−i−i−i−iiiii−i−i−i−iiiii−i−i−i−i11-1-11-111-1-1ii−i−i1-1
χ101111-1-1-1-1-1-1111-1-111111-1-1-1-11-1-1-1iiii−i−i−i−i1111-1-11111-1-1-1-1−i−iii1-1−i−i−i−iiiiiiiii−i−i−i−iiiii−i−i−i−i11-1-1-11-1-111−i−iii-11
χ111111-1-1-1-1-1-1111-1-111111-1-1-1-11-1-1-1iiii−i−i−i−i1111-1-1-1-1-1-11111ii−i−i1-1iiii−i−i−i−iiiii−i−i−i−i−i−i−i−iiiii-1-1111-111-1-1−i−iii-11
χ121111-1-1-1-1-1-1111-1-111111-1-1-1-11-1-1-1iiii−i−i−i−i1111-1-1-1-1-1-11111−i−iii1-1−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−iiiii-1-111-11-1-111ii−i−i1-1
χ131111-1-1-1-1-1-1111-1-111111-1-1-1-11-1-1-1−i−i−i−iiiii1111-1-11111-1-1-1-1ii−i−i1-1iiii−i−i−i−i−i−i−i−iiiii−i−i−i−iiiii11-1-1-11-1-111ii−i−i-11
χ141111-1-1-1-1-1-1111-1-111111-1-1-1-11-1-1-1−i−i−i−iiiii1111-1-11111-1-1-1-1−i−iii1-1−i−i−i−iiiii−i−i−i−iiiii−i−i−i−iiiii11-1-11-111-1-1−i−iii1-1
χ151111-1-1-1-1-1-1111-1-111111-1-1-1-11-1-1-1−i−i−i−iiiii1111-1-1-1-1-1-11111ii−i−i1-1iiii−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−i-1-111-11-1-111−i−iii1-1
χ161111-1-1-1-1-1-1111-1-111111-1-1-1-11-1-1-1−i−i−i−iiiii1111-1-1-1-1-1-11111−i−iii1-1−i−i−i−iiiii−i−i−i−iiiiiiiii−i−i−i−i-1-1111-111-1-1ii−i−i-11
χ172222222222222-2-2-2-22222222-2-2220000000022-2-2-2-2000000000000-2-2000000000000000022-2-222-2-20000000000000000
χ182222222222222-2-2-2-22222222-2-2220000000022-2-2-2-2000000000000-2-20000000000000000-2-222-2-2220000000000000000
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
χ202222222222-1222222-1-1-1-1-1-1-122-1-122222222-1-1-1-1-1-100000000-2-2-2-2-1-111111111-1-1-1-1-1-1-1-1000000000000-2-21111000000
χ212222222222-1222222-1-1-1-1-1-1-122-1-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1000000002222-1-1-1-1-1-1-1-1-1-111111111000000000000-2-21111000000
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
χ2322222222-2-22-2-222222222222-2-2-2-200000000-2-22222222222220000-2-2000000000000000000000000-2-2-2-2000000000000
χ2422222222-2-22-2-222222222222-2-2-2-200000000-2-22222-2-2-2-2-2-2-2-20000-2-20000000000000000000000002222000000000000
χ2522222222-2-22-2-2-2-2-2-2222222222-2-22i2i−2i−2i2i2i−2i−2i-2-2-2-2-2-200000000000022000000002i2i−2i−2i2i2i−2i−2i000000000000000000000000
χ2622222222-2-22-2-2-2-2-2-2222222222-2-2−2i−2i2i2i−2i−2i2i2i-2-2-2-2-2-20000000000002200000000−2i−2i2i2i−2i−2i2i2i000000000000000000000000
χ2722222222-2-2-1-2-2-2-2-2-2-1-1-1-1-1-1-122112i2i−2i−2i2i2i−2i−2i111111000000000000-1-133−3−333−3−3−i−iii−i−iii00000000000000−i3i3−i3i3000000
χ2822222222-2-2-1-2-2-2-2-2-2-1-1-1-1-1-1-122112i2i−2i−2i2i2i−2i−2i111111000000000000-1-1−3−333−3−333−i−iii−i−iii00000000000000i3−i3i3−i3000000
χ2922222222-2-2-1-2-2-2-2-2-2-1-1-1-1-1-1-12211−2i−2i2i2i−2i−2i2i2i111111000000000000-1-133−3−333−3−3ii−i−iii−i−i00000000000000i3−i3i3−i3000000
χ3022222222-2-2-1-2-2-2-2-2-2-1-1-1-1-1-1-12211−2i−2i2i2i−2i−2i2i2i111111000000000000-1-1−3−333−3−333ii−i−iii−i−i00000000000000−i3i3−i3i3000000
χ312222-2-2-2-2222-2-222-2-2222-2-2-2-22-22222-2-2-2-222-2-2-2-2220000000000002-20000000022-2-2-2-222000000000000000000000000
χ322222-2-2-2-2222-2-222-2-2222-2-2-2-22-222-2-22222-2-2-2-2-2-2220000000000002-200000000-2-22222-2-2000000000000000000000000
χ332222-2-2-2-2222-2-2-2-222222-2-2-2-2-222200000000-2-222-2-22222-2-2-2-20000-22000000000000000000000000-2-222000000000000
χ342222-2-2-2-2222-2-2-2-222222-2-2-2-2-222200000000-2-222-2-2-2-2-2-222220000-2200000000000000000000000022-2-2000000000000
χ352222-2-2-2-222-1-2-222-2-2-1-1-111112-2-1-122-2-2-2-2221111-1-1000000000000-11−i3−i3i3i3i3i3−i3−i3-1-11111-1-100000000000000−i3i3i3−i3000000
χ362222-2-2-2-222-1-2-222-2-2-1-1-111112-2-1-122-2-2-2-2221111-1-1000000000000-11i3i3−i3−i3−i3−i3i3i3-1-11111-1-100000000000000i3−i3−i3i3000000
χ372222-2-2-2-222-1-2-222-2-2-1-1-111112-2-1-1-2-22222-2-21111-1-1000000000000-11−i3−i3i3i3i3i3−i3−i311-1-1-1-11100000000000000i3−i3−i3i3000000
χ382222-2-2-2-222-1-2-222-2-2-1-1-111112-2-1-1-2-22222-2-21111-1-1000000000000-11i3i3−i3−i3−i3−i3i3i311-1-1-1-11100000000000000−i3i3i3−i3000000
χ392222-2-2-2-2-2-222222-2-2222-2-2-2-2-22-2-20000000022-2-222000000000000-2200000000000000002i2i−2i−2i−2i−2i2i2i0000000000000000
χ402222-2-2-2-2-2-222222-2-2222-2-2-2-2-22-2-20000000022-2-222000000000000-220000000000000000−2i−2i2i2i2i2i−2i−2i0000000000000000
χ412222-2-2-2-2-2-2-122-2-222-1-1-111112-2112i2i2i2i−2i−2i−2i−2i-1-1-1-111000000002i2i−2i−2i-11−i−i−i−iiiii−i−i−i−iiiii0000000000002-2-1-111000000
χ422222-2-2-2-2-2-2-122-2-222-1-1-111112-2112i2i2i2i−2i−2i−2i−2i-1-1-1-11100000000−2i−2i2i2i-11iiii−i−i−i−i−i−i−i−iiiii000000000000-2211-1-1000000
χ432222-2-2-2-2-2-2-122-2-222-1-1-111112-211−2i−2i−2i−2i2i2i2i2i-1-1-1-111000000002i2i−2i−2i-11−i−i−i−iiiiiiiii−i−i−i−i000000000000-2211-1-1000000
χ442222-2-2-2-2-2-2-122-2-222-1-1-111112-211−2i−2i−2i−2i2i2i2i2i-1-1-1-11100000000−2i−2i2i2i-11iiii−i−i−i−iiiii−i−i−i−i0000000000002-2-1-111000000
χ4522-2-222-2-22-222-200002-2-222-2-2002-22−22−22−22−22-2000022−2−222−2−2000000000000002−22−22−22−2002-2002-22−22−2000000000000
χ4622-2-222-2-22-222-200002-2-222-2-2002-22−22−22−22−22-20000−2−222−2−222000000000000002−22−22−22−200-2200-22−22−22000000000000
χ4722-2-222-2-22-222-200002-2-222-2-2002-2−22−22−22−222-2000022−2−222−2−200000000000000−22−22−22−2200-2200-222−22−2000000000000
χ4822-2-222-2-22-222-200002-2-222-2-2002-2−22−22−22−222-20000−2−222−2−22200000000000000−22−22−22−22002-2002-2−22−22000000000000
χ4922-2-222-2-2-222-2200002-2-222-2-200-22−i2i2i2−i2−i2i2i2−i2-22000022−2−222−2−200000000000000−i2i2i2−i2−i2i2i2−i22i−2i002i−2i00−22−22000000000000
χ5022-2-222-2-2-222-2200002-2-222-2-200-22−i2i2i2−i2−i2i2i2−i2-220000−2−222−2−22200000000000000−i2i2i2−i2−i2i2i2−i2−2i2i00−2i2i002−22−2000000000000
χ5122-2-222-2-2-222-2200002-2-222-2-200-22i2−i2−i2i2i2−i2−i2i2-22000022−2−222−2−200000000000000i2−i2−i2i2i2−i2−i2i2−2i2i00−2i2i00−22−22000000000000
χ5222-2-222-2-2-222-2200002-2-222-2-200-22i2−i2−i2i2i2−i2−i2i2-220000−2−222−2−22200000000000000i2−i2−i2i2i2−i2−i2i22i−2i002i−2i002−22−2000000000000
χ5322-2-2-2-2222-22-2200002-2-2-2-222002-22−2−22−222−2-22000022−2−2−2−222000000000000002−2−22−222−2-22002-200−222−2000000000000
χ5422-2-2-2-2222-22-2200002-2-2-2-222002-22−2−22−222−2-220000−2−22222−2−2000000000000002−2−22−222−22-200-22002−2−22000000000000
χ5522-2-2-2-2222-22-2200002-2-2-2-222002-2−222−22−2−22-22000022−2−2−2−22200000000000000−222−22−2−222-200-2200−222−2000000000000
χ5622-2-2-2-2222-22-2200002-2-2-2-222002-2−222−22−2−22-220000−2−22222−2−200000000000000−222−22−2−22-22002-2002−2−22000000000000
χ5722-2-2-2-222-2222-200002-2-2-2-22200-22−i2i2−i2i2i2−i2i2−i22-2000022−2−2−2−22200000000000000−i2i2−i2i2i2−i2i2−i200−2i2i002i−2i2−2−22000000000000
χ5822-2-2-2-222-2222-200002-2-2-2-22200-22−i2i2−i2i2i2−i2i2−i22-20000−2−22222−2−200000000000000−i2i2−i2i2i2−i2i2−i2002i−2i00−2i2i−222−2000000000000
χ5922-2-2-2-222-2222-200002-2-2-2-22200-22i2−i2i2−i2−i2i2−i2i22-2000022−2−2−2−22200000000000000i2−i2i2−i2−i2i2−i2i2002i−2i00−2i2i2−2−22000000000000
χ6022-2-2-2-222-2222-200002-2-2-2-22200-22i2−i2i2−i2−i2i2−i2i22-20000−2−22222−2−200000000000000i2−i2i2−i2−i2i2−i2i200−2i2i002i−2i−222−2000000000000
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χ694444444444-244-4-4-4-4-2-2-2-2-2-2-2-4-4-2-200000000-2-22222000000000000220000000000000000000000000000000000000000
χ7044444444-4-4-2-4-44444-2-2-2-2-2-2-2-4-4220000000022-2-2-2-2000000000000220000000000000000000000000000000000000000
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χ854-44-44i−4i4i−4i00-200−4i4i-442-22−2i2i−2i2i000000000000002-22i−2i00000000000000ζ4−ζ14−ζ20+ζ22−ζ4+ζ14+ζ20−ζ22−ζ4+ζ14+ζ20−ζ22ζ4−ζ14−ζ20+ζ22−ζ4−ζ14+ζ20+ζ22ζ4+ζ14−ζ20−ζ22ζ4+ζ14−ζ20−ζ22−ζ4−ζ14+ζ20+ζ2200000000000000000000000000000000
χ864-44-4−4i4i−4i4i004004i−4i-44-44-4−4i4i−4i4i00000000000000-444i−4i000000000000000000000000000000000000000000000000000000
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χ884-44-4−4i4i−4i4i00-2004i−4i-442-222i−2i2i−2i000000000000002-2−2i2i00000000000000ζ4+ζ14−ζ20−ζ22−ζ4−ζ14+ζ20+ζ22−ζ4−ζ14+ζ20+ζ22ζ4+ζ14−ζ20−ζ22−ζ4+ζ14+ζ20−ζ22ζ4−ζ14−ζ20+ζ22ζ4−ζ14−ζ20+ζ22−ζ4+ζ14+ζ20−ζ2200000000000000000000000000000000
χ894-44-4−4i4i−4i4i00-200−4i4i4-42-222i−2i2i−2i00000000000000-222i−2i000000002−2i−2+2i2+2i−2−2i00−1+i1−i−1+i1−i−1−i1+i−1−i1+i00000000000000000000000000000000
χ904-44-4−4i4i−4i4i00-200−4i4i4-42-222i−2i2i−2i00000000000000-222i−2i00000000−2+2i2−2i−2−2i2+2i001−i−1+i1−i−1+i1+i−1−i1+i−1−i00000000000000000000000000000000
χ914-4-444i−4i−4i4i004000000-4-444i−4i−4i4i00000000000000000022−22−22222i2−2i2−2i22i20000000000000000000000000000000000000000000000
χ924-4-444i−4i−4i4i004000000-4-444i−4i−4i4i000000000000000000−222222−22−2i22i22i2−2i20000000000000000000000000000000000000000000000
χ934-4-44−4i4i4i−4i004000000-4-44−4i4i4i−4i00000000000000000022−22−2222−2i22i22i2−2i20000000000000000000000000000000000000000000000
χ944-4-44−4i4i4i−4i004000000-4-44−4i4i4i−4i000000000000000000−222222−222i2−2i2−2i22i20000000000000000000000000000000000000000000000
χ958-8-888i−8i−8i8i00-400000044-4−4i4i4i−4i000000000000000000000000000000000000000000000000000000000000000000000000
χ968-8-88−8i8i8i−8i00-400000044-44i−4i−4i4i000000000000000000000000000000000000000000000000000000000000000000000000

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