Finite Group Databasebeta

← Group #10694399

Character table — Group #10694399

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90
size1111111122222222222222224444444444444444444444444444444444444416161616161616161616161624242424242424242424242424242424
order122244443444444446661212121224668888888812121212121212121212242424242424242424242424242424242444661212121212128888888888888888
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
χ51111111111111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1
χ61111111111111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111
χ71111111111111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-11111
χ81111111111111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-111111111-1-1-1-1
χ91111-1-1-1-111111-1-1-1-1111-1-1-1-1-11-1-11111-1-1-1-11111-1-1-1-11111111111-1-1-1-1-1-1-1-11-11-111-1-111-1-1ii−i−iii−i−iii−i−iii−i−i
χ101111-1-1-1-111111-1-1-1-1111-1-1-1-1-11-1-11111-1-1-1-11111-1-1-1-11111111111-1-1-1-1-1-1-1-11-11-111-1-111-1-1−i−iii−i−iii−i−iii−i−iii
χ111111-1-1-1-111111-1-1-1-1111-1-1-1-1-11-1-11111-1-1-1-11111-1-1-1-11111111111-1-1-1-1-1-1-1-1-11-11-1-111-1-111ii−i−iii−i−i−i−iii−i−iii
χ121111-1-1-1-111111-1-1-1-1111-1-1-1-1-11-1-11111-1-1-1-11111-1-1-1-11111111111-1-1-1-1-1-1-1-1-11-11-1-111-1-111−i−iii−i−iiiii−i−iii−i−i
χ131111-1-1-1-111111-1-1-1-1111-1-1-1-1-11-1-1-1-1-1-111111111-1-1-1-111-1-1-1-1-1-1-1-1111111111-1-1111-1-1-1-111ii−i−i−i−iiiii−i−i−i−iii
χ141111-1-1-1-111111-1-1-1-1111-1-1-1-1-11-1-1-1-1-1-111111111-1-1-1-111-1-1-1-1-1-1-1-1111111111-1-1111-1-1-1-111−i−iiiii−i−i−i−iiiii−i−i
χ151111-1-1-1-111111-1-1-1-1111-1-1-1-1-11-1-1-1-1-1-111111111-1-1-1-111-1-1-1-1-1-1-1-111111111-111-1-1-11111-1-1ii−i−i−i−iii−i−iiiii−i−i
χ161111-1-1-1-111111-1-1-1-1111-1-1-1-1-11-1-1-1-1-1-111111111-1-1-1-111-1-1-1-1-1-1-1-111111111-111-1-1-11111-1-1−i−iiiii−i−iii−i−i−i−iii
χ1722222222222-2-2-2-2222222222-2-2-2-20000000022-2-222-2-2-2-200000000000000000000000000002-22-2000000000000
χ1822222222222-2-2-2-2222222222-2-2-2-20000000022-2-222-2-2-2-20000000000000000000000000000-22-22000000000000
χ19222222222-2-22222-2-22222222-2-2-2-222-2-222-2-2-2-2-2-2-2-222222222-2-2-2-22222-2-2-2-20000000000000000000000000000
χ20222222222-2-22222-2-22222222-2-2-2-2-2-222-2-222-2-2-2-2-2-22222-2-2-2-22222-2-2-2-222220000000000000000000000000000
χ21222222222-2-2-2-2-2-2-2-22222222222200000000-2-222-2-2-2-2-2-2000000000000000000000000000000002i−2i2i−2i00000000
χ22222222222-2-2-2-2-2-2-2-22222222222200000000-2-222-2-2-2-2-2-200000000000000000000000000000000−2i2i−2i2i00000000
χ2322222222-122222222-1-1-1-1-1-1-122-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-10000000000000000
χ2422222222-122222222-1-1-1-1-1-1-122-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2111111110000000000000000
χ2522222222-122222222-1-1-1-1-1-1-122-1-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-1-1-1111111111111111122-2-2-1-1-1-111110000000000000000
χ2622222222-122222222-1-1-1-1-1-1-122-1-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-1-1-11111111111111111-2-2221111-1-1-1-10000000000000000
χ2722222222-1-2-22222-2-2-1-1-1-1-1-1-1-2-21122-2-222-2-2111111-1-1-1-1-1-1-1-11111-1-1-1-111110000−i3i3−i3i3−i3i3−i3i30000000000000000
χ2822222222-1-2-22222-2-2-1-1-1-1-1-1-1-2-21122-2-222-2-2111111-1-1-1-1-1-1-1-11111-1-1-1-111110000i3−i3i3−i3i3−i3i3−i30000000000000000
χ2922222222-1-2-22222-2-2-1-1-1-1-1-1-1-2-211-2-222-2-222111111-1-1-1-11111-1-1-1-11111-1-1-1-10000−i3i3−i3i3i3−i3i3−i30000000000000000
χ3022222222-1-2-22222-2-2-1-1-1-1-1-1-1-2-211-2-222-2-222111111-1-1-1-11111-1-1-1-11111-1-1-1-10000i3−i3i3−i3−i3i3−i3i30000000000000000
χ312222-2-2-2-2222-2-222-2-2222-2-2-2-22-2220000000022-2-2-2-222-2-200000000000000000000000000002i−2i−2i2i000000000000
χ322222-2-2-2-2222-2-222-2-2222-2-2-2-22-2220000000022-2-2-2-222-2-20000000000000000000000000000−2i2i2i−2i000000000000
χ332222-2-2-2-22-2-222-2-222222-2-2-2-22-22222-2-2-2-222-2-2-2-222-2-2222222-2-2-2-2-2-2-2-222220000000000000000000000000000
χ342222-2-2-2-22-2-222-2-222222-2-2-2-22-222-2-22222-2-2-2-2-2-222-2-222-2-2-2-222222222-2-2-2-20000000000000000000000000000
χ352222-2-2-2-22-2-2-2-22222222-2-2-2-2-22-2-200000000-2-2222222-2-2000000000000000000000000000000002-2-2200000000
χ362222-2-2-2-22-2-2-2-22222222-2-2-2-2-22-2-200000000-2-2222222-2-200000000000000000000000000000000-222-200000000
χ372222-2-2-2-2-12222-2-2-2-2-1-1-11111-22112222-2-2-2-2-1-1-1-11111-1-1-1-1-1-1-1-1-1-1111111112-22-2-1-111-1-1110000000000000000
χ382222-2-2-2-2-12222-2-2-2-2-1-1-11111-22112222-2-2-2-2-1-1-1-11111-1-1-1-1-1-1-1-1-1-111111111-22-2211-1-111-1-10000000000000000
χ392222-2-2-2-2-12222-2-2-2-2-1-1-11111-2211-2-2-2-22222-1-1-1-11111-1-111111111-1-1-1-1-1-1-1-12-2-22-1-11111-1-10000000000000000
χ402222-2-2-2-2-12222-2-2-2-2-1-1-11111-2211-2-2-2-22222-1-1-1-11111-1-111111111-1-1-1-1-1-1-1-1-222-211-1-1-1-1110000000000000000
χ412222-2-2-2-2-1-2-222-2-222-1-1-111112-2-1-122-2-2-2-2221111-1-111-1-1-1-1-1-111111111-1-1-1-10000−i3i3i3−i3−i3i3i3−i30000000000000000
χ422222-2-2-2-2-1-2-222-2-222-1-1-111112-2-1-122-2-2-2-2221111-1-111-1-1-1-1-1-111111111-1-1-1-10000i3−i3−i3i3i3−i3−i3i30000000000000000
χ432222-2-2-2-2-1-2-222-2-222-1-1-111112-2-1-1-2-22222-2-21111-1-111-1-11111-1-1-1-1-1-1-1-111110000−i3i3i3−i3i3−i3−i3i30000000000000000
χ442222-2-2-2-2-1-2-222-2-222-1-1-111112-2-1-1-2-22222-2-21111-1-111-1-11111-1-1-1-1-1-1-1-111110000i3−i3−i3i3−i3i3i3−i30000000000000000
χ4522-2-22i2i−2i−2i2002-22i−2i002-2-22i2i−2i−2i0000002i−2i002-20000002i−2i2-200002i2i−2i−2i000022-2-2000000000000000000001+i−1−i1−i−1+i1−i−1+i1+i−1−i
χ4622-2-22i2i−2i−2i2002-22i−2i002-2-22i2i−2i−2i0000002i−2i002-20000002i−2i2-200002i2i−2i−2i000022-2-200000000000000000000−1−i1+i−1+i1−i−1+i1−i−1−i1+i
χ4722-2-22i2i−2i−2i2002-22i−2i002-2-22i2i−2i−2i000000−2i2i00-220000002i−2i2-20000−2i−2i2i2i0000-2-222000000000000000000001+i−1−i1−i−1+i−1+i1−i−1−i1+i
χ4822-2-22i2i−2i−2i2002-22i−2i002-2-22i2i−2i−2i000000−2i2i00-220000002i−2i2-20000−2i−2i2i2i0000-2-22200000000000000000000−1−i1+i−1+i1−i1−i−1+i1+i−1−i
χ4922-2-2−2i−2i2i2i2002-2−2i2i002-2-2−2i−2i2i2i0000002i−2i00-22000000−2i2i2-200002i2i−2i−2i0000-2-222000000000000000000001−i−1+i1+i−1−i−1−i1+i−1+i1−i
χ5022-2-2−2i−2i2i2i2002-2−2i2i002-2-2−2i−2i2i2i0000002i−2i00-22000000−2i2i2-200002i2i−2i−2i0000-2-22200000000000000000000−1+i1−i−1−i1+i1+i−1−i1−i−1+i
χ5122-2-2−2i−2i2i2i2002-2−2i2i002-2-2−2i−2i2i2i000000−2i2i002-2000000−2i2i2-20000−2i−2i2i2i000022-2-2000000000000000000001−i−1+i1+i−1−i1+i−1−i1−i−1+i
χ5222-2-2−2i−2i2i2i2002-2−2i2i002-2-2−2i−2i2i2i000000−2i2i002-2000000−2i2i2-20000−2i−2i2i2i000022-2-200000000000000000000−1+i1−i−1−i1+i−1−i1+i−1+i1−i
χ5344444444-244-4-4-4-444-2-2-2-2-2-2-2-4-42200000000-2-222-2-2222200000000000000000000000000000000000000000000
χ5444444444-2-4-4-4-4-4-4-4-4-2-2-2-2-2-2-244-2-20000000022-2-222222200000000000000000000000000000000000000000000
χ554444-4-4-4-4-244-4-444-4-4-2-2-222224-4-2-200000000-2-22222-2-22200000000000000000000000000000000000000000000
χ564444-4-4-4-4-2-4-4-4-44444-2-2-22222-44220000000022-2-2-2-2-2-22200000000000000000000000000000000000000000000
χ5744-4-44i4i−4i−4i400-44−4i4i004-4-44i4i−4i−4i000000000000000000−4i4i-4400000000000000000000000000000000000000000000
χ5844-4-44i4i−4i−4i-2004-44i−4i00-222−2i−2i2i2i0000004i−4i004-4000000−2i2i-220000−2i−2i2i2i0000-2-2220000000000000000000000000000
χ5944-4-44i4i−4i−4i-2004-44i−4i00-222−2i−2i2i2i000000−4i4i00-44000000−2i2i-2200002i2i−2i−2i000022-2-20000000000000000000000000000
χ6044-4-44i4i−4i−4i-200-44−4i4i00-222−2i−2i2i2i0000000000000000002i−2i2-22323−23−230000−2i3−2i32i32i300000000000000000000000000000000
χ6144-4-44i4i−4i−4i-200-44−4i4i00-222−2i−2i2i2i0000000000000000002i−2i2-2−23−23232300002i32i3−2i3−2i300000000000000000000000000000000
χ6244-4-4−4i−4i4i4i400-444i−4i004-4-4−4i−4i4i4i0000000000000000004i−4i-4400000000000000000000000000000000000000000000
χ6344-4-4−4i−4i4i4i-2004-4−4i4i00-2222i2i−2i−2i0000004i−4i00-440000002i−2i-220000−2i−2i2i2i000022-2-20000000000000000000000000000
χ6444-4-4−4i−4i4i4i-2004-4−4i4i00-2222i2i−2i−2i000000−4i4i004-40000002i−2i-2200002i2i−2i−2i0000-2-2220000000000000000000000000000
χ6544-4-4−4i−4i4i4i-200-444i−4i00-2222i2i−2i−2i000000000000000000−2i2i2-22323−23−2300002i32i3−2i3−2i300000000000000000000000000000000
χ6644-4-4−4i−4i4i4i-200-444i−4i00-2222i2i−2i−2i000000000000000000−2i2i2-2−23−2323230000−2i3−2i32i32i300000000000000000000000000000000
χ674-44-44-44-4400000000-44-44-44-40000−2i22i200−2i22i2000000000000−2i22i2−2i22i20000−2i22i2−2i22i200000000000000000000000000000000
χ684-44-44-44-4400000000-44-44-44-400002i2−2i2002i2−2i20000000000002i2−2i22i2−2i200002i2−2i22i2−2i200000000000000000000000000000000
χ694-44-44-44-4-2000000002-22-22-2200−2i32i3−2i22i200−2i22i20000−2i32i3000000i2−i2i2−i26−66−6i2−i2i2−i26−66−60000000000000000000000000000
χ704-44-44-44-4-2000000002-22-22-2200−2i32i32i2−2i2002i2−2i20000−2i32i3000000−i2i2−i2i2−66−66−i2i2−i2i2−66−660000000000000000000000000000
χ714-44-44-44-4-2000000002-22-22-22002i3−2i3−2i22i200−2i22i200002i3−2i3000000i2−i2i2−i2−66−66i2−i2i2−i2−66−660000000000000000000000000000
χ724-44-44-44-4-2000000002-22-22-22002i3−2i32i2−2i2002i2−2i200002i3−2i3000000−i2i2−i2i26−66−6−i2i2−i2i26−66−60000000000000000000000000000
χ734-44-4-44-44400000000-44-4-44-440000−2i22i2002i2−2i2000000000000−2i22i2−2i22i200002i2−2i22i2−2i200000000000000000000000000000000
χ744-44-4-44-44400000000-44-4-44-4400002i2−2i200−2i22i20000000000002i2−2i22i2−2i20000−2i22i2−2i22i200000000000000000000000000000000
χ754-44-4-44-44-2000000002-222-22-200−2i32i3−2i22i2002i2−2i200002i3−2i3000000i2−i2i2−i2−66−66−i2i2−i2i26−66−60000000000000000000000000000
χ764-44-4-44-44-2000000002-222-22-200−2i32i32i2−2i200−2i22i200002i3−2i3000000−i2i2−i2i26−66−6i2−i2i2−i2−66−660000000000000000000000000000
χ774-44-4-44-44-2000000002-222-22-2002i3−2i3−2i22i2002i2−2i20000−2i32i3000000i2−i2i2−i26−66−6−i2i2−i2i2−66−660000000000000000000000000000
χ784-44-4-44-44-2000000002-222-22-2002i3−2i32i2−2i200−2i22i20000−2i32i3000000−i2i2−i2i2−66−66i2−i2i2−i26−66−60000000000000000000000000000
χ794-4-444i−4i−4i4i44-400004i−4i-4-444i−4i−4i4i0000000000004-4004i−4i000000000000000000000000000000000000000000000000
χ804-4-444i−4i−4i4i4-440000−4i4i-4-444i−4i−4i4i000000000000-4400−4i4i000000000000000000000000000000000000000000000000
χ814-4-444i−4i−4i4i-24-400004i−4i22-2−2i2i2i−2i000000000000-2200−2i2i0000i6−i6−i6i6i6−i6−i6i66−6−666−6−660000000000000000000000000000
χ824-4-444i−4i−4i4i-24-400004i−4i22-2−2i2i2i−2i000000000000-2200−2i2i0000−i6i6i6−i6−i6i6i6−i6−666−6−666−60000000000000000000000000000
χ834-4-444i−4i−4i4i-2-440000−4i4i22-2−2i2i2i−2i0000000000002-2002i−2i0000i6−i6−i6i6−i6i6i6−i66−6−66−666−60000000000000000000000000000
χ844-4-444i−4i−4i4i-2-440000−4i4i22-2−2i2i2i−2i0000000000002-2002i−2i0000−i6i6i6−i6i6−i6−i6i6−666−66−6−660000000000000000000000000000
χ854-4-44−4i4i4i−4i44-40000−4i4i-4-44−4i4i4i−4i0000000000004-400−4i4i000000000000000000000000000000000000000000000000
χ864-4-44−4i4i4i−4i4-4400004i−4i-4-44−4i4i4i−4i000000000000-44004i−4i000000000000000000000000000000000000000000000000
χ874-4-44−4i4i4i−4i-24-40000−4i4i22-22i−2i−2i2i000000000000-22002i−2i0000i6−i6−i6i6i6−i6−i6i6−666−6−666−60000000000000000000000000000
χ884-4-44−4i4i4i−4i-24-40000−4i4i22-22i−2i−2i2i000000000000-22002i−2i0000−i6i6i6−i6−i6i6i6−i66−6−666−6−660000000000000000000000000000
χ894-4-44−4i4i4i−4i-2-4400004i−4i22-22i−2i−2i2i0000000000002-200−2i2i0000i6−i6−i6i6−i6i6i6−i6−666−66−6−660000000000000000000000000000
χ904-4-44−4i4i4i−4i-2-4400004i−4i22-22i−2i−2i2i0000000000002-200−2i2i0000−i6i6i6−i6i6−i6−i6i66−6−66−666−60000000000000000000000000000

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