Finite Group Databasebeta

← Group #10831850

Character table — Group #10831850

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90
size11112222222222222222224444444444444444444444444444444444444488881212121216161616161616161616242424242424242424244848
order122222222234444666666622224444446666666666661212121212121212121212121212121244442244441212121212121212444444444444
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-11-1-11-1-11111-1-1
χ4111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-111-1-1-1-111
χ51111111111111111111111-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-111-1-1-1-111111111-1-1-1-1-1-1
χ61111111111111111111111-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-111-1-1-1-111-1-1-1-1-1-1111111
χ71111111111111111111111-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-11111-1-11-1-11-1-1-1-1-1-111
χ81111111111111111111111-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-111-1111111-1-1
χ911111111111-1-1-1-111111111111-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-11-111111-11-111-1-11-1-11-1-11-111-1-11-1
χ1011111111111-1-1-1-111111111111-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-11-1-1-1-1-11-11-111-1-11-11-111-11-1-111-11
χ1111111111111-1-1-1-111111111111-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-111111-11-11-1-111-11-1-11-1-1111-1-1-11
χ1211111111111-1-1-1-111111111111-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-11-1-1-1-1-11-11-1-111-1111-111-1-1-1111-1
χ1311111111111-1-1-1-11111111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111-11-11111-111-1-1-1111-1-11-1-11-1-1-111-11
χ1411111111111-1-1-1-11111111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111-11-1-1-1-1-1-111-1-1-1111-11-111-1111-1-11-1
χ1511111111111-1-1-1-11111111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-11-1111111-1-1111-1-1-11-1-11-1-11-1-1111-1
χ1611111111111-1-1-1-11111111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-11-11-1-1-1-11-1-1111-1-1-1111-111-111-1-1-11
χ172222222222-12222-1-1-1-1-1-1-12222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12222000022-1-1-1-1-1-1-1-1000000000000
χ182222222222-12222-1-1-1-1-1-1-12222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-20000-2-211111111000000000000
χ192222222222-12222-1-1-1-1-1-1-1-2-2-2-222-2-2-2-2-1-1-1-111111111-1-1-1-1-1-1-1-11111111122220000-2-2-1-11111-1-1000000000000
χ202222222222-12222-1-1-1-1-1-1-1-2-2-2-222-2-2-2-2-1-1-1-111111111-1-1-1-1-1-1-1-111111111-2-2-2-200002211-1-1-1-111000000000000
χ212222222222-1-2-2-2-2-1-1-1-1-1-1-12222-2-2-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1-111111111111111112-22-200002-2-11-1-111-11000000000000
χ222222222222-1-2-2-2-2-1-1-1-1-1-1-12222-2-2-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-22-220000-221-111-1-11-1000000000000
χ232222222222-1-2-2-2-2-1-1-1-1-1-1-1-2-2-2-2-2-22222-1-1-1-11111111111111111-1-1-1-1-1-1-1-12-22-20000-22-1111-1-1-11000000000000
χ242222222222-1-2-2-2-2-1-1-1-1-1-1-1-2-2-2-2-2-22222-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-22-2200002-21-1-1-1111-1000000000000
χ2522222-22-2-2-2222-2-2222222200002-20000-2-2-2-2000000002222-2-2-2-20000000022-2-2000000220000-2-2000000000000
χ2622222-22-2-2-2222-2-2222222200002-20000-2-2-2-2000000002222-2-2-2-200000000-2-222000000-2-2000022000000000000
χ2722222-22-2-2-22-2-22222222220000-220000-2-2-2-200000000-2-2-2-22222000000002-2-220000002-20000-22000000000000
χ2822222-22-2-2-22-2-22222222220000-220000-2-2-2-200000000-2-2-2-2222200000000-222-2000000-2200002-2000000000000
χ2922222-22-2-2-2-122-2-2-1-1-1-1-1-1-100002-200001111−i3−i3−i3−i3i3i3i3i3-1-1-1-11111−i3−i3−i3−i3i3i3i3i322-2-2000000-1-1−i3i3−i3i311000000000000
χ3022222-22-2-2-2-122-2-2-1-1-1-1-1-1-100002-200001111−i3−i3−i3−i3i3i3i3i3-1-1-1-11111−i3−i3−i3−i3i3i3i3i3-2-22200000011i3−i3i3−i3-1-1000000000000
χ3122222-22-2-2-2-122-2-2-1-1-1-1-1-1-100002-200001111i3i3i3i3−i3−i3−i3−i3-1-1-1-11111i3i3i3i3−i3−i3−i3−i322-2-2000000-1-1i3−i3i3−i311000000000000
χ3222222-22-2-2-2-122-2-2-1-1-1-1-1-1-100002-200001111i3i3i3i3−i3−i3−i3−i3-1-1-1-11111i3i3i3i3−i3−i3−i3−i3-2-22200000011−i3i3−i3i3-1-1000000000000
χ3322222-22-2-2-2-1-2-222-1-1-1-1-1-1-10000-2200001111−i3−i3−i3−i3i3i3i3i31111-1-1-1-1i3i3i3i3−i3−i3−i3−i32-2-22000000-11−i3i3i3−i31-1000000000000
χ3422222-22-2-2-2-1-2-222-1-1-1-1-1-1-10000-2200001111−i3−i3−i3−i3i3i3i3i31111-1-1-1-1i3i3i3i3−i3−i3−i3−i3-222-20000001-1i3−i3−i3i3-11000000000000
χ3522222-22-2-2-2-1-2-222-1-1-1-1-1-1-10000-2200001111i3i3i3i3−i3−i3−i3−i31111-1-1-1-1−i3−i3−i3−i3i3i3i3i32-2-22000000-11i3−i3−i3i31-1000000000000
χ3622222-22-2-2-2-1-2-222-1-1-1-1-1-1-10000-2200001111i3i3i3i3−i3−i3−i3−i31111-1-1-1-1−i3−i3−i3−i3i3i3i3i3-222-20000001-1−i3i3i3−i3-11000000000000
χ372222-22-2-2-22222-2-22-2-22-2-220000-22000022-2-20000000022-2-222-2-2000000000000000000000000000220-2-2000000
χ382222-22-2-2-22222-2-22-2-22-2-220000-22000022-2-20000000022-2-222-2-2000000000000000000000000000-2-2022000000
χ392222-22-2-2-222-2-2222-2-22-2-2200002-2000022-2-200000000-2-222-2-2220000000000000000000000000002-20-22000000
χ402222-22-2-2-222-2-2222-2-22-2-2200002-2000022-2-200000000-2-222-2-222000000000000000000000000000-2202-2000000
χ412222-2-2-222-2222222-2-22-2-220000-2-20000-2-2220000000022-2-2-2-22200000000000022-2-20000000000-200200000000
χ422222-2-2-222-2222222-2-22-2-220000-2-20000-2-2220000000022-2-2-2-222000000000000-2-2220000000000200-200000000
χ432222-2-2-222-22-2-2-2-22-2-22-2-220000220000-2-22200000000-2-22222-2-200000000000022-2-20000000000200-200000000
χ442222-2-2-222-22-2-2-2-22-2-22-2-220000220000-2-22200000000-2-22222-2-2000000000000-2-2220000000000-200200000000
χ4522-2-222-22-2-220000222-2-2-2-222-2-20000002-22-222-2-222-2-2000000000000000000002-22-200000000000000002-20000
χ4622-2-222-22-2-220000222-2-2-2-222-2-20000002-22-222-2-222-2-200000000000000000000-22-220000000000000000-220000
χ4722-2-222-22-2-220000222-2-2-2-2-2-2220000002-22-2-2-222-2-222000000000000000000002-22-20000000000000000-220000
χ4822-2-222-22-2-220000222-2-2-2-2-2-2220000002-22-2-2-222-2-22200000000000000000000-22-2200000000000000002-20000
χ4922-2-2-2-222-22200002-2-2-222-20000002i2i−2i−2i-222-200000000000000002i2i−2i−2i2i2i−2i−2i00002-2-220000000000000000002i−2i00
χ5022-2-2-2-222-22200002-2-2-222-20000002i2i−2i−2i-222-200000000000000002i2i−2i−2i2i2i−2i−2i0000-222-2000000000000000000−2i2i00
χ5122-2-2-2-222-22200002-2-2-222-2000000−2i−2i2i2i-222-20000000000000000−2i−2i2i2i−2i−2i2i2i00002-2-22000000000000000000−2i2i00
χ5222-2-2-2-222-22200002-2-2-222-2000000−2i−2i2i2i-222-20000000000000000−2i−2i2i2i−2i−2i2i2i0000-222-20000000000000000002i−2i00
χ534444-44-4-4-44-244-4-4-222-222-20000-440000-2-22200000000-2-222-2-22200000000000000000000000000000000000000
χ544444-44-4-4-44-2-4-444-222-222-200004-40000-2-2220000000022-2-222-2-200000000000000000000000000000000000000
χ554444-4-4-444-4-24444-222-222-20000-4-4000022-2-200000000-2-22222-2-200000000000000000000000000000000000000
χ564444-4-4-444-4-2-4-4-4-4-222-222-2000044000022-2-20000000022-2-2-2-22200000000000000000000000000000000000000
χ5744-4-444-44-4-4-20000-2-2-2222244-4-4000000-22-22-2-222-2-2220000000000000000000000000000000000000000000000
χ5844-4-444-44-4-4-20000-2-2-22222-4-444000000-22-2222-2-222-2-20000000000000000000000000000000000000000000000
χ5944-4-44-4-4-44440000444-4-4-4-40000000000-44-44000000000000000000000000000000000000000000000000000000
χ6044-4-44-4-4-444-20000-2-2-2222200000000002-22-2−2i3−2i32i32i32i32i3−2i3−2i30000000000000000000000000000000000000000000000
χ6144-4-44-4-4-444-20000-2-2-2222200000000002-22-22i32i3−2i3−2i3−2i3−2i32i32i30000000000000000000000000000000000000000000000
χ6244-4-4-444-44-4400004-4-4-444-400000000004-4-44000000000000000000000000000000000000000000000000000000
χ6344-4-4-444-44-4-20000-2222-2-220000000000-222-200000000000000002323−23−23−23−232323000000000000000000000000000000
χ6444-4-4-444-44-4-20000-2222-2-220000000000-222-20000000000000000−23−2323232323−23−23000000000000000000000000000000
χ6544-4-4-4-444-44-20000-2222-2-220000004i4i−4i−4i2-2-220000000000000000−2i−2i2i2i−2i−2i2i2i000000000000000000000000000000
χ6644-4-4-4-444-44-20000-2222-2-22000000−4i−4i4i4i2-2-2200000000000000002i2i−2i−2i2i2i−2i−2i000000000000000000000000000000
χ674-44-40000004004i−4i-400400-42-22-2002i−2i2i−2i00002-22-22-22-20000004i−4i2i−2i2i−2i2i−2i2i−2i000000000000000000000000000000
χ684-44-40000004004i−4i-400400-4-22-2200−2i2i−2i2i0000-22-22-22-220000004i−4i−2i2i−2i2i−2i2i−2i2i000000000000000000000000000000
χ694-44-4000000400−4i4i-400400-42-22-200−2i2i−2i2i00002-22-22-22-2000000−4i4i−2i2i−2i2i−2i2i−2i2i000000000000000000000000000000
χ704-44-4000000400−4i4i-400400-4-22-22002i−2i2i−2i0000-22-22-22-22000000−4i4i2i−2i2i−2i2i−2i2i−2i000000000000000000000000000000
χ714-44-4000000-2004i−4i2−2i32i3-2−2i32i322-22-2002i−2i2i−2i0000−1−i31+i3−1−i31+i3−1+i31−i3−1+i31−i3000023−23−2i2i2ζ7−2ζ72ζ7−2ζ72ζ11−2ζ112ζ11−2ζ11000000000000000000000000000000
χ724-44-4000000-2004i−4i2−2i32i3-2−2i32i32-22-2200−2i2i−2i2i00001+i3−1−i31+i3−1−i31−i3−1+i31−i3−1+i3000023−23−2i2i−2ζ72ζ7−2ζ72ζ7−2ζ112ζ11−2ζ112ζ11000000000000000000000000000000
χ734-44-4000000-2004i−4i22i3−2i3-22i3−2i322-22-2002i−2i2i−2i0000−1+i31−i3−1+i31−i3−1−i31+i3−1−i31+i30000−2323−2i2i2ζ11−2ζ112ζ11−2ζ112ζ7−2ζ72ζ7−2ζ7000000000000000000000000000000
χ744-44-4000000-2004i−4i22i3−2i3-22i3−2i32-22-2200−2i2i−2i2i00001−i3−1+i31−i3−1+i31+i3−1−i31+i3−1−i30000−2323−2i2i−2ζ112ζ11−2ζ112ζ11−2ζ72ζ7−2ζ72ζ7000000000000000000000000000000
χ754-44-4000000-200−4i4i2−2i32i3-2−2i32i322-22-200−2i2i−2i2i0000−1−i31+i3−1−i31+i3−1+i31−i3−1+i31−i30000−23232i−2i−2ζ72ζ7−2ζ72ζ7−2ζ112ζ11−2ζ112ζ11000000000000000000000000000000
χ764-44-4000000-200−4i4i2−2i32i3-2−2i32i32-22-22002i−2i2i−2i00001+i3−1−i31+i3−1−i31−i3−1+i31−i3−1+i30000−23232i−2i2ζ7−2ζ72ζ7−2ζ72ζ11−2ζ112ζ11−2ζ11000000000000000000000000000000
χ774-44-4000000-200−4i4i22i3−2i3-22i3−2i322-22-200−2i2i−2i2i0000−1+i31−i3−1+i31−i3−1−i31+i3−1−i31+i3000023−232i−2i−2ζ112ζ11−2ζ112ζ11−2ζ72ζ7−2ζ72ζ7000000000000000000000000000000
χ784-44-4000000-200−4i4i22i3−2i3-22i3−2i32-22-22002i−2i2i−2i00001−i3−1+i31−i3−1+i31+i3−1−i31+i3−1−i3000023−232i−2i2ζ11−2ζ112ζ11−2ζ112ζ7−2ζ72ζ7−2ζ7000000000000000000000000000000
χ794-4-4400000044-400-400-40042-2-22002-2-2200002-2-222-2-224-40000002-2-222-2-22000000000000000000000000000000
χ804-4-4400000044-400-400-4004-222-200-222-20000-222-2-222-24-4000000-222-2-222-2000000000000000000000000000000
χ814-4-440000004-4400-400-40042-2-2200-222-200002-2-222-2-22-44000000-222-2-222-2000000000000000000000000000000
χ824-4-440000004-4400-400-4004-222-2002-2-220000-222-2-222-2-440000002-2-222-2-22000000000000000000000000000000
χ834-4-44000000-24-4002−2i32i322i3−2i3-22-2-22002-2-220000−1−i31+i31+i3−1−i3−1+i31−i31−i3−1+i3-22−2i32i30000−1−i31+i31+i3−1−i3−1+i31−i31−i3−1+i3000000000000000000000000000000
χ844-4-44000000-24-4002−2i32i322i3−2i3-2-222-200-222-200001+i3−1−i3−1−i31+i31−i3−1+i3−1+i31−i3-22−2i32i300001+i3−1−i3−1−i31+i31−i3−1+i3−1+i31−i3000000000000000000000000000000
χ854-4-44000000-24-40022i3−2i32−2i32i3-22-2-22002-2-220000−1+i31−i31−i3−1+i3−1−i31+i31+i3−1−i3-222i3−2i30000−1+i31−i31−i3−1+i3−1−i31+i31+i3−1−i3000000000000000000000000000000
χ864-4-44000000-24-40022i3−2i32−2i32i3-2-222-200-222-200001−i3−1+i3−1+i31−i31+i3−1−i3−1−i31+i3-222i3−2i300001−i3−1+i3−1+i31−i31+i3−1−i3−1−i31+i3000000000000000000000000000000
χ874-4-44000000-2-44002−2i32i322i3−2i3-22-2-2200-222-20000−1−i31+i31+i3−1−i3−1+i31−i31−i3−1+i32-22i3−2i300001+i3−1−i3−1−i31+i31−i3−1+i3−1+i31−i3000000000000000000000000000000
χ884-4-44000000-2-44002−2i32i322i3−2i3-2-222-2002-2-2200001+i3−1−i3−1−i31+i31−i3−1+i3−1+i31−i32-22i3−2i30000−1−i31+i31+i3−1−i3−1+i31−i31−i3−1+i3000000000000000000000000000000
χ894-4-44000000-2-440022i3−2i32−2i32i3-22-2-2200-222-20000−1+i31−i31−i3−1+i3−1−i31+i31+i3−1−i32-2−2i32i300001−i3−1+i3−1+i31−i31+i3−1−i3−1−i31+i3000000000000000000000000000000
χ904-4-44000000-2-440022i3−2i32−2i32i3-2-222-2002-2-2200001−i3−1+i3−1+i31−i31+i3−1−i3−1−i31+i32-2−2i32i30000−1+i31−i31−i3−1+i3−1−i31+i31+i3−1−i3000000000000000000000000000000

Here ζ is a primitive root of unity of order 12 (ζ12 = 1); i = ζ3.