Finite Group Databasebeta

← Group #10848614

Character table — Group #10848614

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90
size11112222222222222222224444444444444444444444444444444444444488881212121216161616161616161616242424242424242424244848
order12222234444444466666664444444444121212121212121212121212121212121212121212121212121212124444444422666612121212244444888888
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1
χ4111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111
χ5111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-11111111111-1-1-1-1-1-1
χ6111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1111111
χ7111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111111111-1-1-1-111-1-1-1-1-1-1-1-111
χ8111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-111111111-1-1
χ911111111-1-1-1-11111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1111111-1-111111-111-1-111-1-1-1-111-1-111-1-11-1
χ1011111111-1-1-1-11111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-11-111-1-111-1-111-1-111-1-111-11
χ1111111111-1-1-1-11111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1111111-11-1-111-1-111-1-1-1-11111-1-1-11
χ1211111111-1-1-1-11111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-111-1-1-1-1-11-1-111-1-1111111-1-1-1-1111-1
χ1311111111-1-1-1-11111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111-1-11111-11-1-11111-1-1-1-111-1-1-1-111-11
χ1411111111-1-1-1-11111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-1-11-1-11111-1-111-1-11111-1-11-1
χ1511111111-1-1-1-11111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-11111111-111-1-1-1-111-1-1-1-111-1-1111-1
χ1611111111-1-1-1-11111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-111-1-1-1-11-111-1-1-1-1111111-1-111-1-1-11
χ172222222-222-2-2-2-2-222222222-2000000002222-2-2-2-20000000000000000-2-2-2-22-22-200000000002-22-2000000000000
χ182222222-222-2-2-2-2-222222222-2000000002222-2-2-2-20000000000000000-2-2-2-2-22-220000000000-22-22000000000000
χ192222222-2-2-222-2-2-22222222-2200000000-2-2-2-222220000000000000000-2-2-2-22-2-2200000000002-2-22000000000000
χ202222222-2-2-222-2-2-22222222-2200000000-2-2-2-222220000000000000000-2-2-2-2-222-20000000000-222-2000000000000
χ21222222-122222222-1-1-1-1-1-1-12222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12222000022-1-1-1-1-1-1-1-1000000000000
χ22222222-122222222-1-1-1-1-1-1-12222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-20000-2-211111111000000000000
χ23222222-122222222-1-1-1-1-1-1-122-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-11111111111111111-1-1-1-122220000-2-21111-1-1-1-1000000000000
χ24222222-122222222-1-1-1-1-1-1-122-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-2-2-2-2000022-1-1-1-11111000000000000
χ25222222-12-2-2-2-2222-1-1-1-1-1-1-1-2-22222-2-2-2-211111111-1-1-1-1-1-1-1-111111111-1-1-1-122-2-200002-2-1-111-1-111000000000000
χ26222222-12-2-2-2-2222-1-1-1-1-1-1-1-2-22222-2-2-2-211111111-1-1-1-1-1-1-1-111111111-1-1-1-1-2-2220000-2211-1-111-1-1000000000000
χ27222222-12-2-2-2-2222-1-1-1-1-1-1-1-2-2-2-2-2-222221111111111111111-1-1-1-1-1-1-1-1-1-1-1-122-2-20000-2211-1-1-1-111000000000000
χ28222222-12-2-2-2-2222-1-1-1-1-1-1-1-2-2-2-2-2-222221111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-2-22200002-2-1-11111-1-1000000000000
χ29222222-1-222-2-2-2-2-2-1-1-1-1-1-1-12-200000000-1-1-1-11111−i3−i3−i3−i3i3i3i3i3−i3−i3−i3−i3i3i3i3i311112-22-2000000−i3i3−i3i3-11-11000000000000
χ30222222-1-222-2-2-2-2-2-1-1-1-1-1-1-12-200000000-1-1-1-11111−i3−i3−i3−i3i3i3i3i3−i3−i3−i3−i3i3i3i3i31111-22-22000000i3−i3i3−i31-11-1000000000000
χ31222222-1-222-2-2-2-2-2-1-1-1-1-1-1-12-200000000-1-1-1-11111i3i3i3i3−i3−i3−i3−i3i3i3i3i3−i3−i3−i3−i311112-22-2000000i3−i3i3−i3-11-11000000000000
χ32222222-1-222-2-2-2-2-2-1-1-1-1-1-1-12-200000000-1-1-1-11111i3i3i3i3−i3−i3−i3−i3i3i3i3i3−i3−i3−i3−i31111-22-22000000−i3i3−i3i31-11-1000000000000
χ33222222-1-2-2-222-2-2-2-1-1-1-1-1-1-1-22000000001111-1-1-1-1−i3−i3−i3−i3i3i3i3i3i3i3i3i3−i3−i3−i3−i311112-2-22000000−i3i3i3−i3-111-1000000000000
χ34222222-1-2-2-222-2-2-2-1-1-1-1-1-1-1-22000000001111-1-1-1-1−i3−i3−i3−i3i3i3i3i3i3i3i3i3−i3−i3−i3−i31111-222-2000000i3−i3−i3i31-1-11000000000000
χ35222222-1-2-2-222-2-2-2-1-1-1-1-1-1-1-22000000001111-1-1-1-1i3i3i3i3−i3−i3−i3−i3−i3−i3−i3−i3i3i3i3i311112-2-22000000i3−i3−i3i3-111-1000000000000
χ36222222-1-2-2-222-2-2-2-1-1-1-1-1-1-1-22000000001111-1-1-1-1i3i3i3i3−i3−i3−i3−i3−i3−i3−i3−i3i3i3i3i31111-222-2000000−i3i3i3−i31-1-11000000000000
χ372222-2-22222-2-2-2-2222-2-2-2-22-220000000022-2-222-2-2000000000000000022-2-2000022-2-200000000002-20000000000
χ382222-2-22222-2-2-2-2222-2-2-2-22-220000000022-2-222-2-2000000000000000022-2-20000-2-2220000000000-220000000000
χ392222-2-222-2-222-2-2222-2-2-2-222-200000000-2-222-2-222000000000000000022-2-2000022-2-20000000000-220000000000
χ402222-2-222-2-222-2-2222-2-2-2-222-200000000-2-222-2-222000000000000000022-2-20000-2-22200000000002-20000000000
χ412222-2-22-2222222-222-2-2-2-22-2-20000000022-2-2-2-2220000000000000000-2-222000000000000000000002-22-2000000
χ422222-2-22-2222222-222-2-2-2-22-2-20000000022-2-2-2-2220000000000000000-2-22200000000000000000000-22-22000000
χ432222-2-22-2-2-2-2-222-222-2-2-2-222200000000-2-22222-2-20000000000000000-2-222000000000000000000002-2-22000000
χ442222-2-22-2-2-2-2-222-222-2-2-2-222200000000-2-22222-2-20000000000000000-2-22200000000000000000000-222-2000000
χ4522-2-22-22200002-2-2-2-222-2-2200000022-2-2000000000000000022-2-222-2-22-22-200002i−2i2i−2i0000000000000000002i−2i00
χ4622-2-22-22200002-2-2-2-222-2-2200000022-2-2000000000000000022-2-222-2-22-22-20000−2i2i−2i2i000000000000000000−2i2i00
χ4722-2-22-22200002-2-2-2-222-2-22000000-2-2220000000000000000-2-222-2-2222-22-200002i−2i2i−2i000000000000000000−2i2i00
χ4822-2-22-22200002-2-2-2-222-2-22000000-2-2220000000000000000-2-222-2-2222-22-20000−2i2i−2i2i0000000000000000002i−2i00
χ4922-2-2-22220000-22-2-2-2-2-22220022-2-200000000000022-2-222-2-2000000002-2-2200002i−2i−2i2i00000000000000002i−2i0000
χ5022-2-2-22220000-22-2-2-2-2-22220022-2-200000000000022-2-222-2-2000000002-2-220000−2i2i2i−2i0000000000000000−2i2i0000
χ5122-2-2-22220000-22-2-2-2-2-222200-2-222000000000000-2-222-2-222000000002-2-2200002i−2i−2i2i0000000000000000−2i2i0000
χ5222-2-2-22220000-22-2-2-2-2-222200-2-222000000000000-2-222-2-222000000002-2-220000−2i2i2i−2i00000000000000002i−2i0000
χ534444-4-4-2444-4-4-4-44-2-22222-2-4400000000-2-222-2-2220000000000000000-2-222000000000000000000000000000000
χ544444-4-4-24-4-444-4-44-2-22222-24-40000000022-2-222-2-20000000000000000-2-222000000000000000000000000000000
χ554444-4-4-2-4444444-4-2-22222-2-4-400000000-2-22222-2-2000000000000000022-2-2000000000000000000000000000000
χ564444-4-4-2-4-4-4-4-444-4-2-22222-2440000000022-2-2-2-222000000000000000022-2-2000000000000000000000000000000
χ5744-4-44-44-40000-444-4-444-4-440000000000000000000000000000000000-44-44000000000000000000000000000000
χ5844-4-44-4-2400004-4-422-2-222-200000044-4-40000000000000000-2-222-2-222-22-22000000000000000000000000000000
χ5944-4-44-4-2400004-4-422-2-222-2000000-4-444000000000000000022-2-222-2-2-22-22000000000000000000000000000000
χ6044-4-44-4-2-40000-44422-2-222-200000000000000000000000000−2i3−2i32i32i32i32i3−2i3−2i32-22-2000000000000000000000000000000
χ6144-4-44-4-2-40000-44422-2-222-2000000000000000000000000002i32i3−2i3−2i3−2i3−2i32i32i32-22-2000000000000000000000000000000
χ6244-4-4-444-400004-44-4-4-4-44440000000000000000000000000000000000-444-4000000000000000000000000000000
χ6344-4-4-44-240000-44-42222-2-2-20044-4-4000000000000-2-222-2-22200000000-222-2000000000000000000000000000000
χ6444-4-4-44-240000-44-42222-2-2-200-4-44400000000000022-2-222-2-200000000-222-2000000000000000000000000000000
χ6544-4-4-44-2-400004-442222-2-2-2000000000000000000−2i3−2i32i32i32i32i3−2i3−2i3000000002-2-22000000000000000000000000000000
χ6644-4-4-44-2-400004-442222-2-2-20000000000000000002i32i3−2i3−2i3−2i3−2i32i32i3000000002-2-22000000000000000000000000000000
χ674-44-40040004-40004-40000-4002i−2i2i−2i2i−2i2i−2i0000004-42i−2i2i−2i2i−2i2i−2i2i−2i2i−2i2i−2i2i−2i0000000000000000000000000000000000
χ684-44-40040004-40004-40000-400−2i2i−2i2i−2i2i−2i2i0000004-4−2i2i−2i2i−2i2i−2i2i−2i2i−2i2i−2i2i−2i2i0000000000000000000000000000000000
χ694-44-4004000-440004-40000-4002i−2i2i−2i−2i2i−2i2i000000-442i−2i2i−2i2i−2i2i−2i−2i2i−2i2i−2i2i−2i2i0000000000000000000000000000000000
χ704-44-4004000-440004-40000-400−2i2i−2i2i2i−2i2i−2i000000-44−2i2i−2i2i−2i2i−2i2i2i−2i2i−2i2i−2i2i−2i0000000000000000000000000000000000
χ714-44-400-20004-4000-22−2i32i3−2i32i32002i−2i2i−2i2i−2i2i−2i0000−2i32i3-222ζ7−2ζ72ζ7−2ζ72ζ11−2ζ112ζ11−2ζ112ζ11−2ζ112ζ11−2ζ112ζ7−2ζ72ζ7−2ζ70000000000000000000000000000000000
χ724-44-400-20004-4000-22−2i32i3−2i32i3200−2i2i−2i2i−2i2i−2i2i0000−2i32i3-22−2ζ72ζ7−2ζ72ζ7−2ζ112ζ11−2ζ112ζ11−2ζ112ζ11−2ζ112ζ11−2ζ72ζ7−2ζ72ζ70000000000000000000000000000000000
χ734-44-400-20004-4000-222i3−2i32i3−2i32002i−2i2i−2i2i−2i2i−2i00002i3−2i3-222ζ11−2ζ112ζ11−2ζ112ζ7−2ζ72ζ7−2ζ72ζ7−2ζ72ζ7−2ζ72ζ11−2ζ112ζ11−2ζ110000000000000000000000000000000000
χ744-44-400-20004-4000-222i3−2i32i3−2i3200−2i2i−2i2i−2i2i−2i2i00002i3−2i3-22−2ζ112ζ11−2ζ112ζ11−2ζ72ζ7−2ζ72ζ7−2ζ72ζ7−2ζ72ζ7−2ζ112ζ11−2ζ112ζ110000000000000000000000000000000000
χ754-44-400-2000-44000-22−2i32i3−2i32i32002i−2i2i−2i−2i2i−2i2i00002i3−2i32-22ζ7−2ζ72ζ7−2ζ72ζ11−2ζ112ζ11−2ζ11−2ζ112ζ11−2ζ112ζ11−2ζ72ζ7−2ζ72ζ70000000000000000000000000000000000
χ764-44-400-2000-44000-22−2i32i3−2i32i3200−2i2i−2i2i2i−2i2i−2i00002i3−2i32-2−2ζ72ζ7−2ζ72ζ7−2ζ112ζ11−2ζ112ζ112ζ11−2ζ112ζ11−2ζ112ζ7−2ζ72ζ7−2ζ70000000000000000000000000000000000
χ774-44-400-2000-44000-222i3−2i32i3−2i32002i−2i2i−2i−2i2i−2i2i0000−2i32i32-22ζ11−2ζ112ζ11−2ζ112ζ7−2ζ72ζ7−2ζ7−2ζ72ζ7−2ζ72ζ7−2ζ112ζ11−2ζ112ζ110000000000000000000000000000000000
χ784-44-400-2000-44000-222i3−2i32i3−2i3200−2i2i−2i2i2i−2i2i−2i0000−2i32i32-2−2ζ112ζ11−2ζ112ζ11−2ζ72ζ7−2ζ72ζ72ζ7−2ζ72ζ7−2ζ72ζ11−2ζ112ζ11−2ζ110000000000000000000000000000000000
χ794-4-4400404-400000-440000-4002i−2i−2i2i2i−2i−2i2i4-40000002i−2i−2i2i2i−2i−2i2i2i−2i−2i2i2i−2i−2i2i0000000000000000000000000000000000
χ804-4-4400404-400000-440000-400−2i2i2i−2i−2i2i2i−2i4-4000000−2i2i2i−2i−2i2i2i−2i−2i2i2i−2i−2i2i2i−2i0000000000000000000000000000000000
χ814-4-440040-4400000-440000-4002i−2i−2i2i−2i2i2i−2i-440000002i−2i−2i2i2i−2i−2i2i−2i2i2i−2i−2i2i2i−2i0000000000000000000000000000000000
χ824-4-440040-4400000-440000-400−2i2i2i−2i2i−2i−2i2i-44000000−2i2i2i−2i−2i2i2i−2i2i−2i−2i2i2i−2i−2i2i0000000000000000000000000000000000
χ834-4-4400-204-4000002-2−2i32i32i3−2i32002i−2i−2i2i2i−2i−2i2i-22−2i32i300002ζ11−2ζ11−2ζ112ζ112ζ7−2ζ7−2ζ72ζ72ζ11−2ζ11−2ζ112ζ112ζ7−2ζ7−2ζ72ζ70000000000000000000000000000000000
χ844-4-4400-204-4000002-2−2i32i32i3−2i3200−2i2i2i−2i−2i2i2i−2i-22−2i32i30000−2ζ112ζ112ζ11−2ζ11−2ζ72ζ72ζ7−2ζ7−2ζ112ζ112ζ11−2ζ11−2ζ72ζ72ζ7−2ζ70000000000000000000000000000000000
χ854-4-4400-204-4000002-22i3−2i3−2i32i32002i−2i−2i2i2i−2i−2i2i-222i3−2i300002ζ7−2ζ7−2ζ72ζ72ζ11−2ζ11−2ζ112ζ112ζ7−2ζ7−2ζ72ζ72ζ11−2ζ11−2ζ112ζ110000000000000000000000000000000000
χ864-4-4400-204-4000002-22i3−2i3−2i32i3200−2i2i2i−2i−2i2i2i−2i-222i3−2i30000−2ζ72ζ72ζ7−2ζ7−2ζ112ζ112ζ11−2ζ11−2ζ72ζ72ζ7−2ζ7−2ζ112ζ112ζ11−2ζ110000000000000000000000000000000000
χ874-4-4400-20-44000002-2−2i32i32i3−2i32002i−2i−2i2i−2i2i2i−2i2-22i3−2i300002ζ11−2ζ11−2ζ112ζ112ζ7−2ζ7−2ζ72ζ7−2ζ112ζ112ζ11−2ζ11−2ζ72ζ72ζ7−2ζ70000000000000000000000000000000000
χ884-4-4400-20-44000002-2−2i32i32i3−2i3200−2i2i2i−2i2i−2i−2i2i2-22i3−2i30000−2ζ112ζ112ζ11−2ζ11−2ζ72ζ72ζ7−2ζ72ζ11−2ζ11−2ζ112ζ112ζ7−2ζ7−2ζ72ζ70000000000000000000000000000000000
χ894-4-4400-20-44000002-22i3−2i3−2i32i32002i−2i−2i2i−2i2i2i−2i2-2−2i32i300002ζ7−2ζ7−2ζ72ζ72ζ11−2ζ11−2ζ112ζ11−2ζ72ζ72ζ7−2ζ7−2ζ112ζ112ζ11−2ζ110000000000000000000000000000000000
χ904-4-4400-20-44000002-22i3−2i3−2i32i3200−2i2i2i−2i2i−2i−2i2i2-2−2i32i30000−2ζ72ζ72ζ7−2ζ7−2ζ112ζ112ζ11−2ζ112ζ7−2ζ7−2ζ72ζ72ζ11−2ζ11−2ζ112ζ110000000000000000000000000000000000

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