Finite Group Databasebeta

← Group #10713681

Character table — Group #10713681

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90
size1111222222222222222222222244444444444444444444444444444444444416161616161616161616161624242424242424242424242424242424
order1222223444444446666666888844888888121212121212121212121212242424242424242424242424242424242244666612121212888888881616161616161616
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
χ51111111-1-1-1-1111111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-111-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1
χ61111111-1-1-1-1111111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-111-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111
χ71111111-1-1-1-1111111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-11111
χ81111111-1-1-1-1111111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-111111111-1-1-1-1
χ91111-1-1111-1-111-1-1-1-1-1-1111-1-1-1-11-11111-1-11111-1-1-1-1-1-1111111-1-1-1-11111-1-1-1-11-11-111-1-111-1-1ii−i−iii−i−iii−i−iii−i−i
χ101111-1-1111-1-111-1-1-1-1-1-1111-1-1-1-11-11111-1-11111-1-1-1-1-1-1111111-1-1-1-11111-1-1-1-11-11-111-1-111-1-1−i−iii−i−iii−i−iii−i−iii
χ111111-1-1111-1-111-1-1-1-1-1-1111-1-1-1-11-11111-1-11111-1-1-1-1-1-1111111-1-1-1-11111-1-1-1-1-11-11-1-111-1-111ii−i−iii−i−i−i−iii−i−iii
χ121111-1-1111-1-111-1-1-1-1-1-1111-1-1-1-11-11111-1-11111-1-1-1-1-1-1111111-1-1-1-11111-1-1-1-1-11-11-1-111-1-111−i−iii−i−iiiii−i−iii−i−i
χ131111-1-11-1-11111-1-1-1-1-1-1111-1-1-1-1-1111-1-111-1-1-1-11111-1-1111111-1-1-1-1-1-1-1-111111-1-1111-1-1-1-111ii−i−i−i−iiiii−i−i−i−iii
χ141111-1-11-1-11111-1-1-1-1-1-1111-1-1-1-1-1111-1-111-1-1-1-11111-1-1111111-1-1-1-1-1-1-1-111111-1-1111-1-1-1-111−i−iiiii−i−i−i−iiiii−i−i
χ151111-1-11-1-11111-1-1-1-1-1-1111-1-1-1-1-1111-1-111-1-1-1-11111-1-1111111-1-1-1-1-1-1-1-11111-111-1-1-11111-1-1ii−i−i−i−iii−i−iiiii−i−i
χ161111-1-11-1-11111-1-1-1-1-1-1111-1-1-1-1-1111-1-111-1-1-1-11111-1-1111111-1-1-1-1-1-1-1-11111-111-1-1-11111-1-1−i−iiiii−i−iii−i−i−i−iii
χ172222222222222222222222-2-2-2-222-2-2-2-2-2-2222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-20000000000000000000000000000
χ18222222222-2-2-2-2-2-222222220000-2200000022-2-222-2-2-2-2-2-2000000000000000000000000000000000000−i2i2−i2i2−i2i2−i2i2
χ19222222222-2-2-2-2-2-222222220000-2200000022-2-222-2-2-2-2-2-2000000000000000000000000000000000000i2−i2i2−i2i2−i2i2−i2
χ202222222-2-222-2-2-2-2222222200002-2000000-2-222-2-222-2-2-2-2000000000000000000000000000000000000−i2i2−i2i2i2−i2i2−i2
χ212222222-2-222-2-2-2-2222222200002-2000000-2-222-2-222-2-2-2-2000000000000000000000000000000000000i2−i2i2−i2−i2i2−i2i2
χ222222222-2-2-2-222222222222-2-2-2-2-2-2-2-22222-2-2-2-2-2-2-2-22222-2-2-2-2-2-2-2-2222222220000000000000000000000000000
χ23222222-122222222-1-1-1-1-1-1-1222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-10000000000000000
χ24222222-122222222-1-1-1-1-1-1-1222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2111111110000000000000000
χ25222222-122222222-1-1-1-1-1-1-1-2-2-2-222-2-2-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1-111111111111111110000−i3i3−i3i3−i3i3−i3i30000000000000000
χ26222222-122222222-1-1-1-1-1-1-1-2-2-2-222-2-2-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1-111111111111111110000i3−i3i3−i3i3−i3i3−i30000000000000000
χ27222222-1-2-2-2-22222-1-1-1-1-1-1-12222-2-222-2-2-2-211111111-1-1-1-1-1-1-1-1-1-1-1-11111111122-2-2-1-1-1-111110000000000000000
χ28222222-1-2-2-2-22222-1-1-1-1-1-1-12222-2-222-2-2-2-211111111-1-1-1-1-1-1-1-1-1-1-1-111111111-2-2221111-1-1-1-10000000000000000
χ29222222-1-2-2-2-22222-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2222211111111-1-1-1-111111111-1-1-1-1-1-1-1-10000−i3i3−i3i3i3−i3i3−i30000000000000000
χ30222222-1-2-2-2-22222-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2222211111111-1-1-1-111111111-1-1-1-1-1-1-1-10000i3−i3i3−i3−i3i3−i3i30000000000000000
χ312222-2-222222-2-222-2-2-2-22220000-2-200000022-2-2-2-22222-2-20000000000000000000000000000000000002−2−222−2−22
χ322222-2-222222-2-222-2-2-2-22220000-2-200000022-2-2-2-22222-2-2000000000000000000000000000000000000−222−2−222−2
χ332222-2-2222-2-222-2-2-2-2-2-222222222-2-2-2-2-2222222-2-2-2-2-2-222-2-2-2-22222-2-2-2-222220000000000000000000000000000
χ342222-2-22-2-22222-2-2-2-2-2-22222222-22-2-222-2-2-2-2-2-22222-2-222-2-2-2-222222222-2-2-2-20000000000000000000000000000
χ352222-2-22-2-2-2-2-2-222-2-2-2-2222000022000000-2-22222-2-222-2-20000000000000000000000000000000000002−2−22−222−2
χ362222-2-22-2-2-2-2-2-222-2-2-2-2222000022000000-2-22222-2-222-2-2000000000000000000000000000000000000−222−22−2−22
χ372222-2-2-122-2-222-2-21111-1-1-122222-2-2-2-2-222-1-1-1-1111111-1-11111-1-1-1-11111-1-1-1-10000−i3i3i3−i3−i3i3i3−i30000000000000000
χ382222-2-2-122-2-222-2-21111-1-1-122222-2-2-2-2-222-1-1-1-1111111-1-11111-1-1-1-11111-1-1-1-10000i3−i3−i3i3i3−i3−i3i30000000000000000
χ392222-2-2-122-2-222-2-21111-1-1-1-2-2-2-22-22222-2-2-1-1-1-1111111-1-1-1-1-1-11111-1-1-1-111112-22-2-1-111-1-1110000000000000000
χ402222-2-2-122-2-222-2-21111-1-1-1-2-2-2-22-22222-2-2-1-1-1-1111111-1-1-1-1-1-11111-1-1-1-11111-22-2211-1-111-1-10000000000000000
χ412222-2-2-1-2-22222-2-21111-1-1-12222-22-2-222-2-21111-1-1-1-111-1-11111-1-1-1-1-1-1-1-111110000−i3i3i3−i3i3−i3−i3i30000000000000000
χ422222-2-2-1-2-22222-2-21111-1-1-12222-22-2-222-2-21111-1-1-1-111-1-11111-1-1-1-1-1-1-1-111110000i3−i3−i3i3−i3i3i3−i30000000000000000
χ432222-2-2-1-2-22222-2-21111-1-1-1-2-2-2-2-2222-2-2221111-1-1-1-111-1-1-1-1-1-111111111-1-1-1-12-2-22-1-11111-1-10000000000000000
χ442222-2-2-1-2-22222-2-21111-1-1-1-2-2-2-2-2222-2-2221111-1-1-1-111-1-1-1-1-1-111111111-1-1-1-1-222-211-1-1-1-1110000000000000000
χ452-2-222-2200002-22-222-2-2-2-2222-2-2002-20000000000002-22-222-2-222-2-20000000000000000000000002i−2i2i−2i00000000
χ462-2-222-2200002-22-222-2-2-2-2222-2-2002-20000000000002-22-222-2-222-2-2000000000000000000000000−2i2i−2i2i00000000
χ472-2-222-2200002-22-222-2-2-2-22-2-22200-220000000000002-22-2-2-222-2-222000000000000000000002-22-2000000000000
χ482-2-222-2200002-22-222-2-2-2-22-2-22200-220000000000002-22-2-2-222-2-22200000000000000000000-22-22000000000000
χ492-2-22-22200002-2-22-2-222-2-2222-2-200-22000000000000-222-2-2-22222-2-2000000000000000000002i−2i−2i2i000000000000
χ502-2-22-22200002-2-22-2-222-2-2222-2-200-22000000000000-222-2-2-22222-2-200000000000000000000−2i2i2i−2i000000000000
χ512-2-22-22200002-2-22-2-222-2-22-2-222002-2000000000000-222-222-2-2-2-2220000000000000000000000002-2-2200000000
χ522-2-22-22200002-2-22-2-222-2-22-2-222002-2000000000000-222-222-2-2-2-222000000000000000000000000-222-200000000
χ53444444-244-4-4-4-4-4-4-2-2-2-2-2-2-20000-44000000-2-222-2-222222200000000000000000000000000000000000000000000
χ54444444-2-4-444-4-4-4-4-2-2-2-2-2-2-200004-400000022-2-222-2-2222200000000000000000000000000000000000000000000
χ554444-4-4-24444-4-4442222-2-2-20000-4-4000000-2-22222-2-2-2-22200000000000000000000000000000000000000000000
χ564444-4-4-2-4-4-4-4-4-4442222-2-2-200004400000022-2-2-2-222-2-22200000000000000000000000000000000000000000000
χ5744-4-4004004i−4i000000004-4-422−2222−220000−2i22i2000000004i−4i0000000022−2222−22−2i2−2i22i22i200000000000000000000000000000000
χ5844-4-4004004i−4i000000004-4-4−2222−222200002i2−2i2000000004i−4i00000000−2222−22222i22i2−2i2−2i200000000000000000000000000000000
χ5944-4-400400−4i4i000000004-4-422−2222−2200002i2−2i200000000−4i4i0000000022−2222−222i22i2−2i2−2i200000000000000000000000000000000
χ6044-4-400400−4i4i000000004-4-4−2222−22220000−2i22i200000000−4i4i00000000−2222−2222−2i2−2i22i22i200000000000000000000000000000000
χ6144-4-400-2004i−4i0000−2i32i3−2i32i3-22222−2222−220000−2i22i2000023−2300−2i2i0000i6−i6i6−i6−22−22i2i2−i2−i266−6−60000000000000000000000000000
χ6244-4-400-2004i−4i0000−2i32i3−2i32i3-222−2222−222200002i2−2i2000023−2300−2i2i0000−i6i6−i6i62−22−2−i2−i2i2i2−6−6660000000000000000000000000000
χ6344-4-400-2004i−4i00002i3−2i32i3−2i3-22222−2222−220000−2i22i20000−232300−2i2i0000−i6i6−i6i6−22−22i2i2−i2−i2−6−6660000000000000000000000000000
χ6444-4-400-2004i−4i00002i3−2i32i3−2i3-222−2222−222200002i2−2i20000−232300−2i2i0000i6−i6i6−i62−22−2−i2−i2i2i266−6−60000000000000000000000000000
χ6544-4-400-200−4i4i0000−2i32i3−2i32i3-22222−2222−2200002i2−2i20000−2323002i−2i0000i6−i6i6−i6−22−22−i2−i2i2i2−6−6660000000000000000000000000000
χ6644-4-400-200−4i4i0000−2i32i3−2i32i3-222−2222−22220000−2i22i20000−2323002i−2i0000−i6i6−i6i62−22−2i2i2−i2−i266−6−60000000000000000000000000000
χ6744-4-400-200−4i4i00002i3−2i32i3−2i3-22222−2222−2200002i2−2i2000023−23002i−2i0000−i6i6−i6i6−22−22−i2−i2i2i266−6−60000000000000000000000000000
χ6844-4-400-200−4i4i00002i3−2i32i3−2i3-222−2222−22220000−2i22i2000023−23002i−2i0000i6−i6i6−i62−22−2i2i2−i2−i2−6−6660000000000000000000000000000
χ694-44-40044i−4i0000000000-44-422−22−2222000000−2i22i24i−4i0000000000000022−22−22220000−2i22i2−2i22i20000000000000000000000000000
χ704-44-40044i−4i0000000000-44-4−222222−220000002i2−2i24i−4i00000000000000−222222−2200002i2−2i22i2−2i20000000000000000000000000000
χ714-44-4004−4i4i0000000000-44-422−22−22220000002i2−2i2−4i4i0000000000000022−22−222200002i2−2i22i2−2i20000000000000000000000000000
χ724-44-4004−4i4i0000000000-44-4−222222−22000000−2i22i2−4i4i00000000000000−222222−220000−2i22i2−2i22i20000000000000000000000000000
χ734-44-400-24i−4i000000−2i32i32i3−2i32-2222−22−2222000000−2i22i2−2i2i0023−23000000i6−i6−i6i6−222−26−66−6i2−i2i2−i20000000000000000000000000000
χ744-44-400-24i−4i000000−2i32i32i3−2i32-22−222222−220000002i2−2i2−2i2i0023−23000000−i6i6i6−i62−2−22−66−66−i2i2−i2i20000000000000000000000000000
χ754-44-400-24i−4i0000002i3−2i3−2i32i32-2222−22−2222000000−2i22i2−2i2i00−2323000000−i6i6i6−i6−222−2−66−66i2−i2i2−i20000000000000000000000000000
χ764-44-400-24i−4i0000002i3−2i3−2i32i32-22−222222−220000002i2−2i2−2i2i00−2323000000i6−i6−i6i62−2−226−66−6−i2i2−i2i20000000000000000000000000000
χ774-44-400-2−4i4i000000−2i32i32i3−2i32-2222−22−22220000002i2−2i22i−2i00−2323000000i6−i6−i6i6−222−2−66−66−i2i2−i2i20000000000000000000000000000
χ784-44-400-2−4i4i000000−2i32i32i3−2i32-22−222222−22000000−2i22i22i−2i00−2323000000−i6i6i6−i62−2−226−66−6i2−i2i2−i20000000000000000000000000000
χ794-44-400-2−4i4i0000002i3−2i3−2i32i32-2222−22−22220000002i2−2i22i−2i0023−23000000−i6i6i6−i6−222−26−66−6−i2i2−i2i20000000000000000000000000000
χ804-44-400-2−4i4i0000002i3−2i3−2i32i32-22−222222−22000000−2i22i22i−2i0023−23000000i6−i6−i6i62−2−22−66−66i2−i2i2−i20000000000000000000000000000
χ814-4-444-440000-44-4444-4-4-4-4400000000000000000000-44-4400000000000000000000000000000000000000000000
χ824-4-444-4-200004-44-4-2-22222-244-4-4004-4000000000000-22-22-2-222-2-222000000000000000000000000000000000000
χ834-4-444-4-200004-44-4-2-22222-2-4-44400-44000000000000-22-2222-2-222-2-2000000000000000000000000000000000000
χ844-4-444-4-20000-44-44-2-22222-2000000000000000000002-22-200000000−2i32i32i3−2i3−2i32i32i3−2i30000000000000000000000000000
χ854-4-444-4-20000-44-44-2-22222-2000000000000000000002-22-2000000002i3−2i3−2i32i32i3−2i3−2i32i30000000000000000000000000000
χ864-4-44-4440000-444-4-4-444-4-44000000000000000000004-4-4400000000000000000000000000000000000000000000
χ874-4-44-44-200004-4-4422-2-222-244-4-400-440000000000002-2-2222-2-2-2-222000000000000000000000000000000000000
χ884-4-44-44-200004-4-4422-2-222-2-4-444004-40000000000002-2-22-2-22222-2-2000000000000000000000000000000000000
χ894-4-44-44-20000-444-422-2-222-200000000000000000000-222-200000000−2i32i32i3−2i32i3−2i3−2i32i30000000000000000000000000000
χ904-4-44-44-20000-444-422-2-222-200000000000000000000-222-2000000002i3−2i3−2i32i3−2i32i32i3−2i30000000000000000000000000000

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