Finite Group Databasebeta

← Group #10829797

Character table — Group #10829797

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81
size11112222222222222222444444444448888888888888888888888888888881212121216161616242424242424242424244848
order122222344444466666664441212121212121212444444444444121212121212121212121212121212121212444412121212222444888888
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111111111111111-1-1-1-1-1-1
χ411111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1111111
χ51111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111111111-1-1-1-11-1-11-1-11111-1-1
χ61111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-111-111-1-1-1-111
χ71111111111111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-111-1-1-1-11111-1-1-1-11-1-11-1-1-1-1-1-111
χ81111111111111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-111-1111111-1-1
χ91111111-1-111111111111-1-1-1-1-1-1-1111111-1-111-1-111-1-11111-1-1-1-1-1-1-1-1-1-11111111111-1-1-11-1-11-111-1-11-1
χ101111111-1-111111111111-1-1-1-1-1-1-1111111-1-111-1-111-1-11111-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-11-111-11-1-111-11
χ111111111-1-111111111111-1-1-1-1-1-1-1111111-1-1-1-111-1-111-1-1-1-111111111-1-1-1-1-1-1111111-1-1-11-1-11-1-1-111-11
χ121111111-1-111111111111-1-1-1-1-1-1-1111111-1-1-1-111-1-111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111-1-11-111-1111-1-11-1
χ131111111-1-111111111111-1-1-1-1-1-1-11111-1-11111-1-1-1-111-1-1-1-11111-1-1-1-1-1-111111111-1-111-1-11-1-1111-1-1-11
χ141111111-1-111111111111-1-1-1-1-1-1-11111-1-11111-1-1-1-111-1-1-1-11111-1-1-1-1-1-11111-1-1-1-1-1-11111-111-1-1-1111-1
χ151111111-1-111111111111-1-1-1-1-1-1-11111-1-111-1-11111-1-11111-1-1-1-11111-1-1-1-1-1-11111-1-111-1-11-1-11-1-1111-1
χ161111111-1-111111111111-1-1-1-1-1-1-11111-1-111-1-11111-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-111-111-1-1-11
χ17222222222-2-2-2-222222222-2-22222-2-2-2-22-22-200000000000000000000-2-2000000002-22-2000000000000
χ18222222222-2-2-2-222222222-2-22222-2-2-2-2-22-2200000000000000000000-2-200000000-22-22000000000000
χ192222222-2-2-2-2-2-22222222-222-2-2-2-2-2-2-2-22-2-220000000000000000000022000000002-2-22000000000000
χ202222222-2-2-2-2-2-22222222-222-2-2-2-2-2-2-2-2-222-2000000000000000000002200000000-222-2000000000000
χ21222222-1222222-1-1-1-1-1-1-1222-1-1-1-1-1-1-1-1222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000-1-1-1-1000000000000
χ22222222-1222222-1-1-1-1-1-1-1222-1-1-1-1-1-1-1-12222-2-2-2-2-2-2-2-2111111111111-1-111110000-1-1-1-1000000000000
χ23222222-1222222-1-1-1-1-1-1-1222-1-1-1-1-1-1-1-1-2-2-2-22222-2-2-2-211111111-1-1-1-1-1-1-1-1-1-100001111000000000000
χ24222222-1222222-1-1-1-1-1-1-1222-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-22222-1-1-1-1-1-1-1-11111-1-1111100001111000000000000
χ25222222-122-2-2-2-2-1-1-1-1-1-1-12-2-2-1-1-1-111112-22-200000000−i3−i3i3i3−i3−i3i3i3−i3−i3i3i311−i3−i3i3i30000-11-11000000000000
χ26222222-122-2-2-2-2-1-1-1-1-1-1-12-2-2-1-1-1-111112-22-200000000i3i3−i3−i3i3i3−i3−i3i3i3−i3−i311i3i3−i3−i30000-11-11000000000000
χ27222222-122-2-2-2-2-1-1-1-1-1-1-12-2-2-1-1-1-11111-22-2200000000−i3−i3i3i3−i3−i3i3i3i3i3−i3−i311i3i3−i3−i300001-11-1000000000000
χ28222222-122-2-2-2-2-1-1-1-1-1-1-12-2-2-1-1-1-11111-22-2200000000i3i3−i3−i3i3i3−i3−i3−i3−i3i3i311−i3−i3i3i300001-11-1000000000000
χ29222222-1-2-22222-1-1-1-1-1-1-1-2-2-21111-1-1-1-122-2-222-2-222-2-2-1-1-1-11111111111-1-1-1-10000-1-111000000000000
χ30222222-1-2-22222-1-1-1-1-1-1-1-2-2-21111-1-1-1-122-2-2-2-222-2-2221111-1-1-1-1-1-1-1-11111110000-1-111000000000000
χ31222222-1-2-22222-1-1-1-1-1-1-1-2-2-21111-1-1-1-1-2-22222-2-2-2-2221111-1-1-1-1111111-1-1-1-1000011-1-1000000000000
χ32222222-1-2-22222-1-1-1-1-1-1-1-2-2-21111-1-1-1-1-2-222-2-22222-2-2-1-1-1-11111-1-1-1-1111111000011-1-1000000000000
χ33222222-1-2-2-2-2-2-2-1-1-1-1-1-1-1-222111111112-2-2200000000−i3−i3i3i3i3i3−i3−i3i3i3−i3−i3-1-1−i3−i3i3i30000-111-1000000000000
χ34222222-1-2-2-2-2-2-2-1-1-1-1-1-1-1-222111111112-2-2200000000i3i3−i3−i3−i3−i3i3i3−i3−i3i3i3-1-1i3i3−i3−i30000-111-1000000000000
χ35222222-1-2-2-2-2-2-2-1-1-1-1-1-1-1-22211111111-222-200000000−i3−i3i3i3i3i3−i3−i3−i3−i3i3i3-1-1i3i3−i3−i300001-1-11000000000000
χ36222222-1-2-2-2-2-2-2-1-1-1-1-1-1-1-22211111111-222-200000000i3i3−i3−i3−i3−i3i3i3i3i3−i3−i3-1-1−i3−i3i3i300001-1-11000000000000
χ372222-2-22222-2-22-2-22-2-222-22-222-2-222-2-20000000000000000000000002-20000000000000220-2-2000000
χ382222-2-22222-2-22-2-22-2-222-22-222-2-222-2-20000000000000000000000002-20000000000000-2-2022000000
χ392222-2-2222-222-2-2-22-2-222-2-2222-2-2-2-222000000000000000000000000-22000022-2-20000200-200000000
χ402222-2-2222-222-2-2-22-2-222-2-2222-2-2-2-222000000000000000000000000-220000-2-2220000-200200000000
χ412222-2-22-2-22-2-22-2-22-2-2222-22-2-22222-2-2000000000000000000000000-2200000000000002-20-22000000
χ422222-2-22-2-22-2-22-2-22-2-2222-22-2-22222-2-2000000000000000000000000-220000000000000-2202-2000000
χ432222-2-22-2-2-222-2-2-22-2-22222-2-2-222-2-2220000000000000000000000002-2000022-2-20000-200200000000
χ442222-2-22-2-2-222-2-2-22-2-22222-2-2-222-2-2220000000000000000000000002-20000-2-2220000200-200000000
χ452-2-222-2200-22-2222-2-2-22-200000002-22-20000002-20000000000002-22-20000002i−2i2i−2i0000000000002i−2i00
χ462-2-222-2200-22-2222-2-2-22-200000002-22-20000002-20000000000002-22-2000000−2i2i−2i2i000000000000−2i2i00
χ472-2-222-2200-22-2222-2-2-22-200000002-22-2000000-22000000000000-22-220000002i−2i2i−2i000000000000−2i2i00
χ482-2-222-2200-22-2222-2-2-22-200000002-22-2000000-22000000000000-22-22000000−2i2i−2i2i0000000000002i−2i00
χ492-2-22-2220022-2-2-2-2-2222-20000000-222-200002i−2i000000000000000000002i−2i2i−2i2i−2i−2i2i00000000002-20000
χ502-2-22-2220022-2-2-2-2-2222-20000000-222-200002i−2i000000000000000000002i−2i2i−2i−2i2i2i−2i0000000000-220000
χ512-2-22-2220022-2-2-2-2-2222-20000000-222-20000−2i2i00000000000000000000−2i2i−2i2i2i−2i−2i2i0000000000-220000
χ522-2-22-2220022-2-2-2-2-2222-20000000-222-20000−2i2i00000000000000000000−2i2i−2i2i−2i2i2i−2i00000000002-20000
χ534444-4-4-2444-4-4422-222-2-2-44-4-2-222-2-222000000000000000000000000-22000000000000000000000000
χ544444-4-4-244-444-422-222-2-2-4-44-2-22222-2-20000000000000000000000002-2000000000000000000000000
χ554444-4-4-2-4-44-4-4422-222-2-24-4422-2-2-2-2220000000000000000000000002-2000000000000000000000000
χ564444-4-4-2-4-4-444-422-222-2-244-422-2-222-2-2000000000000000000000000-22000000000000000000000000
χ5744-4-40044-4000000400-4-40004-4000000000000002-22-22-22-22-22-2000000000000000000000000000000
χ5844-4-40044-4000000400-4-40004-400000000000000-22-22-22-22-22-22000000000000000000000000000000
χ5944-4-4004-44000000400-4-4000-44000000000000002-2-222-22-2-22-22000000000000000000000000000000
χ6044-4-4004-44000000400-4-4000-4400000000000000-222-2-22-222-22-2000000000000000000000000000000
χ6144-4-400-24-40000−2i32i3-2−2i32i322000-22−2i32i30000000000002-22-2−1−i31+i3−1+i31−i3−1−i31+i3−1+i31−i3000000000000000000000000000000
χ6244-4-400-24-40000−2i32i3-2−2i32i322000-22−2i32i3000000000000-22-221+i3−1−i31−i3−1+i31+i3−1−i31−i3−1+i3000000000000000000000000000000
χ6344-4-400-24-400002i3−2i3-22i3−2i322000-222i3−2i30000000000002-22-2−1+i31−i3−1−i31+i3−1+i31−i3−1−i31+i3000000000000000000000000000000
χ6444-4-400-24-400002i3−2i3-22i3−2i322000-222i3−2i3000000000000-22-221−i3−1+i31+i3−1−i31−i3−1+i31+i3−1−i3000000000000000000000000000000
χ6544-4-400-2-440000−2i32i3-2−2i32i3220002-22i3−2i30000000000002-2-22−1−i31+i3−1+i31−i31+i3−1−i31−i3−1+i3000000000000000000000000000000
χ6644-4-400-2-440000−2i32i3-2−2i32i3220002-22i3−2i3000000000000-222-21+i3−1−i31−i3−1+i3−1−i31+i3−1+i31−i3000000000000000000000000000000
χ6744-4-400-2-4400002i3−2i3-22i3−2i3220002-2−2i32i30000000000002-2-22−1+i31−i3−1−i31+i31−i3−1+i31+i3−1−i3000000000000000000000000000000
χ6844-4-400-2-4400002i3−2i3-22i3−2i3220002-2−2i32i3000000000000-222-21−i3−1+i31+i3−1−i3−1+i31−i3−1−i31+i3000000000000000000000000000000
χ694-4-444-44004-44-444-4-4-44-40000000-44-4400000000000000000000000000000000000000000000000000
χ704-4-444-4-2004-44-4-2-2222-2200000002-22-200000000000000000000−2i32i32i3−2i300000000000000000000000000
χ714-4-444-4-2004-44-4-2-2222-2200000002-22-2000000000000000000002i3−2i3−2i32i300000000000000000000000000
χ724-4-444-4-200-44-44-2-2222-220000000-22-220000004-4000000000000-22-2200000000000000000000000000
χ734-4-444-4-200-44-44-2-2222-220000000-22-22000000-440000000000002-22-200000000000000000000000000
χ744-4-44-44400-4-444-4-4-4444-400000004-4-4400000000000000000000000000000000000000000000000000
χ754-4-44-44-20044-4-4222-2-2-2200000002-2-2200004i−4i00000000000000000000−2i2i−2i2i00000000000000000000
χ764-4-44-44-20044-4-4222-2-2-2200000002-2-220000−4i4i000000000000000000002i−2i2i−2i00000000000000000000
χ774-4-44-44-200-4-444222-2-2-220000000-222-20000000000000000000000000023−23−232300000000000000000000
χ784-4-44-44-200-4-444222-2-2-220000000-222-200000000000000000000000000−232323−2300000000000000000000
χ798-88-800800000000-800-880000000000000000000000000000000000000000000000000000000000000
χ808-88-800-4000000−4i34i344i3−4i34-40000000000000000000000000000000000000000000000000000000000000
χ818-88-800-40000004i3−4i34−4i34i34-40000000000000000000000000000000000000000000000000000000000000

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