Finite Group Databasebeta

← Group #10705607

Character table — Group #10705607

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90
size1111222222222222222222222244444444444444444444444444444444444416161616161616161616161624242424242424242424242424242424
order1222223444444446668888121212124466888888121212121212121212122424242424242424242424242424242444441212121212121212444444441616161616161616
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ411111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ51111111-1-1-1-1-1-1111111111-1-1-1-1-111111-1-1-1-1-1-111-1-1-1-11111111111-1-1-1-1-1-1-1-111-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1
χ61111111-1-1-1-1-1-1111111111-1-1-1-1-111111-1-1-1-1-1-111-1-1-1-11111111111-1-1-1-1-1-1-1-111-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111
χ71111111-1-1-1-1-1-1111111111-1-1-1-1-111111-1-1-1-1-1-111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-11111
χ81111111-1-1-1-1-1-1111111111-1-1-1-1-111111-1-1-1-1-1-111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-111111111-1-1-1-1
χ91111-1-111111-1-111111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-111-1-1111111-1-1-1-11111-1-1-1-11-11-111-1-111-1-1ii−i−iii−i−iii−i−iii−i−i
χ101111-1-111111-1-111111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-111-1-1111111-1-1-1-11111-1-1-1-11-11-111-1-111-1-1−i−iii−i−iii−i−iii−i−iii
χ111111-1-111111-1-111111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-111-1-1111111-1-1-1-11111-1-1-1-1-11-11-1-111-1-111ii−i−iii−i−i−i−iii−i−iii
χ121111-1-111111-1-111111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-111-1-1111111-1-1-1-11111-1-1-1-1-11-11-1-111-1-111−i−iii−i−iiiii−i−iii−i−i
χ131111-1-11-1-1-1-11111111-1-1-1-1-1-1-1-11-1-1-111-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-111111-1-1111-1-1-1-111ii−i−i−i−iiiii−i−i−i−iii
χ141111-1-11-1-1-1-11111111-1-1-1-1-1-1-1-11-1-1-111-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-111111-1-1111-1-1-1-111−i−iiiii−i−i−i−iiiii−i−i
χ151111-1-11-1-1-1-11111111-1-1-1-1-1-1-1-11-1-1-111-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-11111-111-1-1-11111-1-1ii−i−i−i−iii−i−iiiii−i−i
χ161111-1-11-1-1-1-11111111-1-1-1-1-1-1-1-11-1-1-111-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-11111-111-1-1-11111-1-1−i−iiiii−i−iii−i−i−i−iii
χ17222222222222222222-2-2-2-222222222-2-2-2-2-2-22222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-20000000000000000000000000000
χ18222222222-2-2-2-2-2-2222000022222-22200000022-2-2-2-2-2-2-2-20000000000000000000000000000000000002−22−22−22−2
χ19222222222-2-2-2-2-2-2222000022222-22200000022-2-2-2-2-2-2-2-2000000000000000000000000000000000000−22−22−22−22
χ202222222-2-22222-2-22220000-2-2-2-2-2-222000000-2-2-2-22222-2-20000000000000000000000000000000000002−22−2−22−22
χ212222222-2-22222-2-22220000-2-2-2-2-2-222000000-2-2-2-22222-2-2000000000000000000000000000000000000−22−222−22−2
χ222222222-2-2-2-2-2-222222-2-2-2-2-2-2-2-2-2222-2-22222-2-222-2-2-2-222-2-2-2-2-2-2-2-2222222220000000000000000000000000000
χ23222222-122222222-1-1-12222-1-1-1-122-1-1222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-10000000000000000
χ24222222-122222222-1-1-12222-1-1-1-122-1-1222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2111111110000000000000000
χ25222222-122222222-1-1-1-2-2-2-2-1-1-1-122-1-1-2-2-2-2-2-2-1-1-1-1-1-1-1-1-1-111111111111111110000−i3i3−i3i3−i3i3−i3i30000000000000000
χ26222222-122222222-1-1-1-2-2-2-2-1-1-1-122-1-1-2-2-2-2-2-2-1-1-1-1-1-1-1-1-1-111111111111111110000i3−i3i3−i3i3−i3i3−i30000000000000000
χ27222222-1-2-2-2-2-2-222-1-1-122221111-22-1-122-2-2-2-211-1-11111-1-1-1-1-1-1-1-1-1-11111111122-2-2-1-1-1-111110000000000000000
χ28222222-1-2-2-2-2-2-222-1-1-122221111-22-1-122-2-2-2-211-1-11111-1-1-1-1-1-1-1-1-1-111111111-2-2221111-1-1-1-10000000000000000
χ29222222-1-2-2-2-2-2-222-1-1-1-2-2-2-21111-22-1-1-2-2222211-1-11111-1-111111111-1-1-1-1-1-1-1-10000−i3i3−i3i3i3−i3i3−i30000000000000000
χ30222222-1-2-2-2-2-2-222-1-1-1-2-2-2-21111-22-1-1-2-2222211-1-11111-1-111111111-1-1-1-1-1-1-1-10000i3−i3i3−i3−i3i3−i3i30000000000000000
χ312222-2-222222-2-22222222222222-2-2-2-2-2-2-2-222-2-2-2-222-2-222-2-2-2-22222-2-2-2-222220000000000000000000000000000
χ322222-2-2222-2-222-2-222200002222-22-2-2000000-2-222-2-222-2-2000000000000000000000000000000000000−i2i2i2−i2−i2i2i2−i2
χ332222-2-2222-2-222-2-222200002222-22-2-2000000-2-222-2-222-2-2000000000000000000000000000000000000i2−i2−i2i2i2−i2−i2i2
χ342222-2-22-2-222-2-2-2-22220000-2-2-2-222-2-2000000222222-2-2-2-2000000000000000000000000000000000000−i2i2i2−i2i2−i2−i2i2
χ352222-2-22-2-222-2-2-2-22220000-2-2-2-222-2-2000000222222-2-2-2-2000000000000000000000000000000000000i2−i2−i2i2−i2i2i2−i2
χ362222-2-22-2-2-2-222222222222-2-2-2-22-2-2-2-2-222-2-222-2-2-2-22222-2-2-2-222222222-2-2-2-20000000000000000000000000000
χ372222-2-2-12222-2-222-1-1-12222-1-1-1-1-2-211-2-2-2-2221111-1-111-1-11111-1-1-1-11111-1-1-1-10000−i3i3i3−i3−i3i3i3−i30000000000000000
χ382222-2-2-12222-2-222-1-1-12222-1-1-1-1-2-211-2-2-2-2221111-1-111-1-11111-1-1-1-11111-1-1-1-10000i3−i3−i3i3i3−i3−i3i30000000000000000
χ392222-2-2-12222-2-222-1-1-1-2-2-2-2-1-1-1-1-2-2112222-2-21111-1-111-1-1-1-1-1-11111-1-1-1-111112-22-2-1-111-1-1110000000000000000
χ402222-2-2-12222-2-222-1-1-1-2-2-2-2-1-1-1-1-2-2112222-2-21111-1-111-1-1-1-1-1-11111-1-1-1-11111-22-2211-1-111-1-10000000000000000
χ412222-2-2-1-2-2-2-22222-1-1-1222211112-211-2-222-2-2-1-11111-1-1-1-11111-1-1-1-1-1-1-1-111110000−i3i3i3−i3i3−i3−i3i30000000000000000
χ422222-2-2-1-2-2-2-22222-1-1-1222211112-211-2-222-2-2-1-11111-1-1-1-11111-1-1-1-1-1-1-1-111110000i3−i3−i3i3−i3i3i3−i30000000000000000
χ432222-2-2-1-2-2-2-22222-1-1-1-2-2-2-211112-21122-2-222-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-12-2-22-1-11111-1-10000000000000000
χ442222-2-2-1-2-2-2-22222-1-1-1-2-2-2-211112-21122-2-222-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-222-211-1-1-1-1110000000000000000
χ452-22-20022i−2i2i−2i002-2-22-22i2i−2i−2i2i2i−2i−2i000000002-200002i−2i002-200002i2i−2i−2i000022-2-20000000000001+i−1−i1−i−1+i1−i−1+i1+i−1−i00000000
χ462-22-20022i−2i2i−2i002-2-22-22i2i−2i−2i2i2i−2i−2i000000002-200002i−2i002-200002i2i−2i−2i000022-2-2000000000000−1−i1+i−1+i1−i−1+i1−i−1−i1+i00000000
χ472-22-20022i−2i2i−2i002-2-22-2−2i−2i2i2i2i2i−2i−2i00000000-2200002i−2i002-20000−2i−2i2i2i0000-2-2220000000000001−i−1+i1+i−1−i−1−i1+i−1+i1−i00000000
χ482-22-20022i−2i2i−2i002-2-22-2−2i−2i2i2i2i2i−2i−2i00000000-2200002i−2i002-20000−2i−2i2i2i0000-2-222000000000000−1+i1−i−1−i1+i1+i−1−i1−i−1+i00000000
χ492-22-2002−2i2i−2i2i002-2-22-22i2i−2i−2i−2i−2i2i2i00000000-220000−2i2i002-200002i2i−2i−2i0000-2-2220000000000001+i−1−i1−i−1+i−1+i1−i−1−i1+i00000000
χ502-22-2002−2i2i−2i2i002-2-22-22i2i−2i−2i−2i−2i2i2i00000000-220000−2i2i002-200002i2i−2i−2i0000-2-222000000000000−1−i1+i−1+i1−i1−i−1+i1+i−1−i00000000
χ512-22-2002−2i2i−2i2i002-2-22-2−2i−2i2i2i−2i−2i2i2i000000002-20000−2i2i002-20000−2i−2i2i2i000022-2-20000000000001−i−1+i1+i−1−i1+i−1−i1−i−1+i00000000
χ522-22-2002−2i2i−2i2i002-2-22-2−2i−2i2i2i−2i−2i2i2i000000002-20000−2i2i002-20000−2i−2i2i2i000022-2-2000000000000−1+i1−i−1−i1+i−1−i1+i−1+i1−i00000000
χ53444444-244-4-4-4-4-4-4-2-2-20000-2-2-2-24-4-2-2000000-2-22222222200000000000000000000000000000000000000000000
χ54444444-2-4-44444-4-4-2-2-200002222-4-4-2-20000002222-2-2-2-22200000000000000000000000000000000000000000000
χ554444-4-4-244-4-444-4-4-2-2-20000-2-2-2-2-442200000022-2-222-2-22200000000000000000000000000000000000000000000
χ564444-4-4-2-4-444-4-4-4-4-2-2-2000022224422000000-2-2-2-2-2-2222200000000000000000000000000000000000000000000
χ5744-4-44-44000000004-4-422−2222−220000004-422−22000000000000002222−22−2222−2222−22000000000000000000000000000000000000
χ5844-4-44-44000000004-4-4−2222−22220000004-4−222200000000000000−22−222222−2222−2222000000000000000000000000000000000000
χ5944-4-44-4-200000000-22222−2222−22−2i32i3−2i32i300-2222−220000−2i32i300000000−2−222−22−22i6i6−i6−i6i6−i6i6−i60000000000000000000000000000
χ6044-4-44-4-200000000-22222−2222−222i3−2i32i3−2i300-2222−2200002i3−2i300000000−2−222−22−22−i6−i6i6i6−i6i6−i6i60000000000000000000000000000
χ6144-4-44-4-200000000-222−2222−2222−2i32i3−2i32i300-22−22220000−2i32i30000000022−2−22−22−2−i6−i6i6i6−i6i6−i6i60000000000000000000000000000
χ6244-4-44-4-200000000-222−2222−22222i3−2i32i3−2i300-22−222200002i3−2i30000000022−2−22−22−2i6i6−i6−i6i6−i6i6−i60000000000000000000000000000
χ6344-4-4-444000000004-4-422−2222−22000000-44−222200000000000000−22−22222222−2222−22000000000000000000000000000000000000
χ6444-4-4-444000000004-4-4−2222−2222000000-4422−22000000000000002222−22−22−2222−2222000000000000000000000000000000000000
χ6544-4-4-44-200000000-22222−2222−22−2i32i3−2i32i3002-2−222200002i3−2i30000000022−2−2−22−22−i6−i6i6i6i6−i6i6−i60000000000000000000000000000
χ6644-4-4-44-200000000-22222−2222−222i3−2i32i3−2i3002-2−22220000−2i32i30000000022−2−2−22−22i6i6−i6−i6−i6i6−i6i60000000000000000000000000000
χ6744-4-4-44-200000000-222−2222−2222−2i32i3−2i32i3002-222−2200002i3−2i300000000−2−2222−22−2i6i6−i6−i6−i6i6−i6i60000000000000000000000000000
χ6844-4-4-44-200000000-222−2222−22222i3−2i32i3−2i3002-222−220000−2i32i300000000−2−2222−22−2−i6−i6i6i6i6−i6i6−i60000000000000000000000000000
χ694-44-40044i−4i−4i4i00-44-44-400004i4i−4i−4i00000000000000−4i4i00-4400000000000000000000000000000000000000000000
χ704-44-4004−4i4i4i−4i00-44-44-40000−4i−4i4i4i000000000000004i−4i00-4400000000000000000000000000000000000000000000
χ714-44-400-24i−4i4i−4i004-42-224i4i−4i−4i−2i−2i2i2i000000004-40000−2i2i00-220000−2i−2i2i2i0000-2-2220000000000000000000000000000
χ724-44-400-24i−4i4i−4i004-42-22−4i−4i4i4i−2i−2i2i2i00000000-440000−2i2i00-2200002i2i−2i−2i000022-2-20000000000000000000000000000
χ734-44-400-24i−4i−4i4i00-442-220000−2i−2i2i2i000000000000002i−2i002-2−2i32i3−2i32i3000023−2323−2300000000000000000000000000000000
χ744-44-400-24i−4i−4i4i00-442-220000−2i−2i2i2i000000000000002i−2i002-22i3−2i32i3−2i30000−2323−232300000000000000000000000000000000
χ754-44-400-2−4i4i4i−4i00-442-2200002i2i−2i−2i00000000000000−2i2i002-2−2i32i3−2i32i30000−2323−232300000000000000000000000000000000
χ764-44-400-2−4i4i4i−4i00-442-2200002i2i−2i−2i00000000000000−2i2i002-22i3−2i32i3−2i3000023−2323−2300000000000000000000000000000000
χ774-44-400-2−4i4i−4i4i004-42-224i4i−4i−4i2i2i−2i−2i00000000-4400002i−2i00-220000−2i−2i2i2i000022-2-20000000000000000000000000000
χ784-44-400-2−4i4i−4i4i004-42-22−4i−4i4i4i2i2i−2i−2i000000004-400002i−2i00-2200002i2i−2i−2i0000-2-2220000000000000000000000000000
χ794-4-4400400004-400-4-44−2i22i22i2−2i20000000000−2i22i2000000004-4000000−2i22i22i2−2i2−2i22i22i2−2i200000000000000000000000000000000
χ804-4-4400400004-400-4-442i2−2i2−2i22i200000000002i2−2i2000000004-40000002i2−2i2−2i22i22i2−2i2−2i22i200000000000000000000000000000000
χ814-4-440040000-4400-4-44−2i22i22i2−2i200000000002i2−2i200000000-44000000−2i22i22i2−2i22i2−2i2−2i22i200000000000000000000000000000000
χ824-4-440040000-4400-4-442i2−2i2−2i22i20000000000−2i22i200000000-440000002i2−2i2−2i22i2−2i22i22i2−2i200000000000000000000000000000000
χ834-4-4400-200004-40022-2−2i22i22i2−2i223−23−2323000000−2i22i2000023−2300-2200−i6i6i6−i6i2−i2−i2i2i2−i2−i2i2−i6i6i6−i60000000000000000000000000000
χ844-4-4400-200004-40022-2−2i22i22i2−2i2−232323−23000000−2i22i20000−232300-2200i6−i6−i6i6i2−i2−i2i2i2−i2−i2i2i6−i6−i6i60000000000000000000000000000
χ854-4-4400-200004-40022-22i2−2i2−2i22i223−23−23230000002i2−2i2000023−2300-2200i6−i6−i6i6−i2i2i2−i2−i2i2i2−i2i6−i6−i6i60000000000000000000000000000
χ864-4-4400-200004-40022-22i2−2i2−2i22i2−232323−230000002i2−2i20000−232300-2200−i6i6i6−i6−i2i2i2−i2−i2i2i2−i2−i6i6i6−i60000000000000000000000000000
χ874-4-4400-20000-440022-2−2i22i22i2−2i223−23−23230000002i2−2i20000−2323002-200i6−i6−i6i6i2−i2−i2i2−i2i2i2−i2−i6i6i6−i60000000000000000000000000000
χ884-4-4400-20000-440022-2−2i22i22i2−2i2−232323−230000002i2−2i2000023−23002-200−i6i6i6−i6i2−i2−i2i2−i2i2i2−i2i6−i6−i6i60000000000000000000000000000
χ894-4-4400-20000-440022-22i2−2i2−2i22i223−23−2323000000−2i22i20000−2323002-200−i6i6i6−i6−i2i2i2−i2i2−i2−i2i2i6−i6−i6i60000000000000000000000000000
χ904-4-4400-20000-440022-22i2−2i2−2i22i2−232323−23000000−2i22i2000023−23002-200i6−i6−i6i6−i2i2i2−i2i2−i2−i2i2−i6i6i6−i60000000000000000000000000000

Here i is the imaginary unit (i² = −1).