Finite Group Databasebeta

← Group #10697849

Character table — Group #10697849

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84
size111122222222222222222244444444444444444444444444444444444444161616161616161616161616242424242424242448484848
order122222344444444666666644444444441212121212121212121212121212121212121212121212121212121244441212121212121212888888882488
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1
χ4111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ5111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-11111-1-1-1-11111-1-1-1-111-1-1
χ6111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-11111-1-1-1-1-1-1-1-11111-1-111
χ7111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111-1-1-1-111111111-1-1-1-1-1-111
χ8111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111-1-1-1-11111-1-1-1-1111111-1-1
χ92222222222-2-2-2-222222222-2-22222-2-2-2-2222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2000000000000000000000000
χ102222222222-2-2-2-222222222-2-2-2-2-2-222222222-2-2-2-2-2-2-2-222222222-2-2-2-2-2-2-2-2000000000000000000000000
χ112222222-2-2-222-2-2-222222222-200000000-2-2-2-200000000000000002222-2-2-2-2002-2000022-2-2000000000000
χ122222222-2-2-222-2-2-222222222-200000000-2-2-2-200000000000000002222-2-2-2-200-220000-2-222000000000000
χ132222222-2-2-2-2-222-22222222-2200000000-2-2-2-20000000000000000-2-2-2-222222-20022-2-20000000000000000
χ142222222-2-2-2-2-222-22222222-2200000000-2-2-2-20000000000000000-2-2-2-22222-2200-2-2220000000000000000
χ15222222-122222222-1-1-1-1-1-1-12222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1000000000000
χ16222222-122222222-1-1-1-1-1-1-12222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-211111111000000000000
χ17222222-122222222-1-1-1-1-1-1-122-2-2-2-2-2-2-2-2-1-1-1-11111111111111111-1-1-1-1-1-1-1-122-2-2-1-1-1-11111000000000000
χ18222222-122222222-1-1-1-1-1-1-122-2-2-2-2-2-2-2-2-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-2-2221111-1-1-1-1000000000000
χ19222222-1222-2-2-2-22-1-1-1-1-1-1-1-2-22222-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1-111111111111111110000−i3i3−i3i3−i3i3−i3i3000000000000
χ20222222-1222-2-2-2-22-1-1-1-1-1-1-1-2-22222-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1-111111111111111110000i3−i3i3−i3i3−i3i3−i3000000000000
χ21222222-1222-2-2-2-22-1-1-1-1-1-1-1-2-2-2-2-2-22222-1-1-1-111111111-1-1-1-1-1-1-1-1111111110000−i3i3−i3i3i3−i3i3−i3000000000000
χ22222222-1222-2-2-2-22-1-1-1-1-1-1-1-2-2-2-2-2-22222-1-1-1-111111111-1-1-1-1-1-1-1-1111111110000i3−i3i3−i3−i3i3−i3i3000000000000
χ23222222-1-2-2-222-2-2-2-1-1-1-1-1-1-12-2000000001111−i3−i3−i3−i3i3i3i3i3−i3−i3−i3−i3i3i3i3i3-1-1-1-11111002-2−i3i3i3−i3-1-111000000000000
χ24222222-1-2-2-222-2-2-2-1-1-1-1-1-1-12-2000000001111−i3−i3−i3−i3i3i3i3i3−i3−i3−i3−i3i3i3i3i3-1-1-1-1111100-22i3−i3−i3i311-1-1000000000000
χ25222222-1-2-2-222-2-2-2-1-1-1-1-1-1-12-2000000001111i3i3i3i3−i3−i3−i3−i3i3i3i3i3−i3−i3−i3−i3-1-1-1-11111002-2i3−i3−i3i3-1-111000000000000
χ26222222-1-2-2-222-2-2-2-1-1-1-1-1-1-12-2000000001111i3i3i3i3−i3−i3−i3−i3i3i3i3i3−i3−i3−i3−i3-1-1-1-1111100-22−i3i3i3−i311-1-1000000000000
χ27222222-1-2-2-2-2-222-2-1-1-1-1-1-1-1-22000000001111−i3−i3−i3−i3i3i3i3i3i3i3i3i3−i3−i3−i3−i31111-1-1-1-12-200-1-111−i3i3i3−i3000000000000
χ28222222-1-2-2-2-2-222-2-1-1-1-1-1-1-1-22000000001111−i3−i3−i3−i3i3i3i3i3i3i3i3i3−i3−i3−i3−i31111-1-1-1-1-220011-1-1i3−i3−i3i3000000000000
χ29222222-1-2-2-2-2-222-2-1-1-1-1-1-1-1-22000000001111i3i3i3i3−i3−i3−i3−i3−i3−i3−i3−i3i3i3i3i31111-1-1-1-12-200-1-111i3−i3−i3i3000000000000
χ30222222-1-2-2-2-2-222-2-1-1-1-1-1-1-1-22000000001111i3i3i3i3−i3−i3−i3−i3−i3−i3−i3−i3i3i3i3i31111-1-1-1-1-220011-1-1−i3i3i3−i3000000000000
χ312222-2-2222-22222-22-2-2-2-222-2-20000000022-2-2000000000000000022-2-222-2-2000000000000000000002-200
χ322222-2-2222-22222-22-2-2-2-222-2-20000000022-2-2000000000000000022-2-222-2-200000000000000000000-2200
χ332222-2-2222-2-2-2-2-2-22-2-2-2-222220000000022-2-20000000000000000-2-222-2-22200000000000000000000002i−2i
χ342222-2-2222-2-2-2-2-2-22-2-2-2-222220000000022-2-20000000000000000-2-222-2-2220000000000000000000000−2i2i
χ352222-2-22-2-2222-2-222-2-2-2-222-2200000000-2-222000000000000000022-2-2-2-222000000000000000022-2-20000
χ362222-2-22-2-2222-2-222-2-2-2-222-2200000000-2-222000000000000000022-2-2-2-2220000000000000000-2-2220000
χ372222-2-22-2-22-2-22222-2-2-2-2222-200000000-2-2220000000000000000-2-22222-2-200000000000022-2-200000000
χ382222-2-22-2-22-2-22222-2-2-2-2222-200000000-2-2220000000000000000-2-22222-2-2000000000000-2-22200000000
χ392-2-222-222-2-200002222-2-2-2-200000022-2-22-22-20000000022-2-222-2-200000000000000000000−i2i2−i2i2−i2i2−i2i20000
χ402-2-222-222-2-200002222-2-2-2-200000022-2-22-22-20000000022-2-222-2-200000000000000000000i2−i2i2−i2i2−i2i2−i20000
χ412-2-222-222-2-200002222-2-2-2-2000000-2-2222-22-200000000-2-222-2-22200000000000000000000−i2i2−i2i2i2−i2i2−i20000
χ422-2-222-222-2-200002222-2-2-2-2000000-2-2222-22-200000000-2-222-2-22200000000000000000000i2−i2i2−i2−i2i2−i2i20000
χ432-2-22-222-22-2000022-2-222-2-20022-2-20000-222-222-2-222-2-20000000000000000000000000000−i2i2i2−i2−i2i2i2−i20000
χ442-2-22-222-22-2000022-2-222-2-20022-2-20000-222-222-2-222-2-20000000000000000000000000000i2−i2−i2i2i2−i2−i2i20000
χ452-2-22-222-22-2000022-2-222-2-200-2-2220000-222-2-2-222-2-2220000000000000000000000000000−i2i2i2−i2i2−i2−i2i20000
χ462-2-22-222-22-2000022-2-222-2-200-2-2220000-222-2-2-222-2-2220000000000000000000000000000i2−i2−i2i2−i2i2i2−i20000
χ474444-4-4-244-44444-4-22222-2-2-4-400000000-2-2220000000000000000-2-222-2-222000000000000000000000000
χ484444-4-4-244-4-4-4-4-4-4-22222-2-24400000000-2-222000000000000000022-2-222-2-2000000000000000000000000
χ494444-4-4-2-4-4444-4-44-22222-2-2-440000000022-2-20000000000000000-2-22222-2-2000000000000000000000000
χ504444-4-4-2-4-44-4-4444-22222-2-24-40000000022-2-2000000000000000022-2-2-2-222000000000000000000000000
χ5144-4-4004000004-40-400004-4002i−2i2i−2i2i−2i2i−2i00002i−2i2i−2i2i−2i2i−2i2i−2i2i−2i2i−2i2i−2i00004-400000000000000000000000000
χ5244-4-4004000004-40-400004-400−2i2i−2i2i−2i2i−2i2i0000−2i2i−2i2i−2i2i−2i2i−2i2i−2i2i−2i2i−2i2i00004-400000000000000000000000000
χ5344-4-400400000-440-400004-4002i−2i2i−2i−2i2i−2i2i00002i−2i2i−2i2i−2i2i−2i−2i2i−2i2i−2i2i−2i2i0000-4400000000000000000000000000
χ5444-4-400400000-440-400004-400−2i2i−2i2i2i−2i2i−2i0000−2i2i−2i2i−2i2i−2i2i2i−2i2i−2i2i−2i2i−2i0000-4400000000000000000000000000
χ5544-4-400-2000004-402−2i32i3−2i32i3-22002i−2i2i−2i2i−2i2i−2i00002ζ14−2ζ142ζ14−2ζ142ζ22−2ζ222ζ22−2ζ222ζ22−2ζ222ζ22−2ζ222ζ14−2ζ142ζ14−2ζ140000-22−2i32i3000000000000000000000000
χ5644-4-400-2000004-402−2i32i3−2i32i3-2200−2i2i−2i2i−2i2i−2i2i0000−2ζ142ζ14−2ζ142ζ14−2ζ222ζ22−2ζ222ζ22−2ζ222ζ22−2ζ222ζ22−2ζ142ζ14−2ζ142ζ140000-22−2i32i3000000000000000000000000
χ5744-4-400-2000004-4022i3−2i32i3−2i3-22002i−2i2i−2i2i−2i2i−2i00002ζ22−2ζ222ζ22−2ζ222ζ14−2ζ142ζ14−2ζ142ζ14−2ζ142ζ14−2ζ142ζ22−2ζ222ζ22−2ζ220000-222i3−2i3000000000000000000000000
χ5844-4-400-2000004-4022i3−2i32i3−2i3-2200−2i2i−2i2i−2i2i−2i2i0000−2ζ222ζ22−2ζ222ζ22−2ζ142ζ14−2ζ142ζ14−2ζ142ζ14−2ζ142ζ14−2ζ222ζ22−2ζ222ζ220000-222i3−2i3000000000000000000000000
χ5944-4-400-200000-4402−2i32i3−2i32i3-22002i−2i2i−2i−2i2i−2i2i00002ζ14−2ζ142ζ14−2ζ142ζ22−2ζ222ζ22−2ζ22−2ζ222ζ22−2ζ222ζ22−2ζ142ζ14−2ζ142ζ1400002-22i3−2i3000000000000000000000000
χ6044-4-400-200000-4402−2i32i3−2i32i3-2200−2i2i−2i2i2i−2i2i−2i0000−2ζ142ζ14−2ζ142ζ14−2ζ222ζ22−2ζ222ζ222ζ22−2ζ222ζ22−2ζ222ζ14−2ζ142ζ14−2ζ1400002-22i3−2i3000000000000000000000000
χ6144-4-400-200000-44022i3−2i32i3−2i3-22002i−2i2i−2i−2i2i−2i2i00002ζ22−2ζ222ζ22−2ζ222ζ14−2ζ142ζ14−2ζ14−2ζ142ζ14−2ζ142ζ14−2ζ222ζ22−2ζ222ζ2200002-2−2i32i3000000000000000000000000
χ6244-4-400-200000-44022i3−2i32i3−2i3-2200−2i2i−2i2i2i−2i2i−2i0000−2ζ222ζ22−2ζ222ζ22−2ζ142ζ14−2ζ142ζ142ζ14−2ζ142ζ14−2ζ142ζ22−2ζ222ζ22−2ζ2200002-2−2i32i3000000000000000000000000
χ634-44-40040004-4000-40000-44002i−2i−2i2i2i−2i−2i2i00002i−2i−2i2i2i−2i−2i2i2i−2i−2i2i2i−2i−2i2i4-4000000000000000000000000000000
χ644-44-40040004-4000-40000-4400−2i2i2i−2i−2i2i2i−2i0000−2i2i2i−2i−2i2i2i−2i−2i2i2i−2i−2i2i2i−2i4-4000000000000000000000000000000
χ654-44-4004000-44000-40000-44002i−2i−2i2i−2i2i2i−2i00002i−2i−2i2i2i−2i−2i2i−2i2i2i−2i−2i2i2i−2i-44000000000000000000000000000000
χ664-44-4004000-44000-40000-4400−2i2i2i−2i2i−2i−2i2i0000−2i2i2i−2i−2i2i2i−2i2i−2i−2i2i2i−2i−2i2i-44000000000000000000000000000000
χ674-44-400-20004-40002−2i32i32i3−2i32-2002i−2i−2i2i2i−2i−2i2i00002ζ22−2ζ22−2ζ222ζ222ζ14−2ζ14−2ζ142ζ142ζ22−2ζ22−2ζ222ζ222ζ14−2ζ14−2ζ142ζ14-22−2i32i30000000000000000000000000000
χ684-44-400-20004-40002−2i32i32i3−2i32-200−2i2i2i−2i−2i2i2i−2i0000−2ζ222ζ222ζ22−2ζ22−2ζ142ζ142ζ14−2ζ14−2ζ222ζ222ζ22−2ζ22−2ζ142ζ142ζ14−2ζ14-22−2i32i30000000000000000000000000000
χ694-44-400-20004-400022i3−2i3−2i32i32-2002i−2i−2i2i2i−2i−2i2i00002ζ14−2ζ14−2ζ142ζ142ζ22−2ζ22−2ζ222ζ222ζ14−2ζ14−2ζ142ζ142ζ22−2ζ22−2ζ222ζ22-222i3−2i30000000000000000000000000000
χ704-44-400-20004-400022i3−2i3−2i32i32-200−2i2i2i−2i−2i2i2i−2i0000−2ζ142ζ142ζ14−2ζ14−2ζ222ζ222ζ22−2ζ22−2ζ142ζ142ζ14−2ζ14−2ζ222ζ222ζ22−2ζ22-222i3−2i30000000000000000000000000000
χ714-44-400-2000-440002−2i32i32i3−2i32-2002i−2i−2i2i−2i2i2i−2i00002ζ22−2ζ22−2ζ222ζ222ζ14−2ζ14−2ζ142ζ14−2ζ222ζ222ζ22−2ζ22−2ζ142ζ142ζ14−2ζ142-22i3−2i30000000000000000000000000000
χ724-44-400-2000-440002−2i32i32i3−2i32-200−2i2i2i−2i2i−2i−2i2i0000−2ζ222ζ222ζ22−2ζ22−2ζ142ζ142ζ14−2ζ142ζ22−2ζ22−2ζ222ζ222ζ14−2ζ14−2ζ142ζ142-22i3−2i30000000000000000000000000000
χ734-44-400-2000-4400022i3−2i3−2i32i32-2002i−2i−2i2i−2i2i2i−2i00002ζ14−2ζ14−2ζ142ζ142ζ22−2ζ22−2ζ222ζ22−2ζ142ζ142ζ14−2ζ14−2ζ222ζ222ζ22−2ζ222-2−2i32i30000000000000000000000000000
χ744-44-400-2000-4400022i3−2i3−2i32i32-200−2i2i2i−2i2i−2i−2i2i0000−2ζ142ζ142ζ14−2ζ14−2ζ222ζ222ζ22−2ζ222ζ14−2ζ14−2ζ142ζ142ζ22−2ζ22−2ζ222ζ222-2−2i32i30000000000000000000000000000
χ754-4-444-44-4440000-4444-4-4-4-40000000000-44-44000000000000000000000000000000000000000000000000
χ764-4-444-4-24-4-400004-2-2-2222200000044-4-4-22-2200000000-2-222-2-22200000000000000000000000000000000
χ774-4-444-4-24-4-400004-2-2-22222000000-4-444-22-220000000022-2-222-2-200000000000000000000000000000000
χ784-4-444-4-2-4440000-4-2-2-2222200000000002-22-200000000−2i3−2i32i32i32i32i3−2i3−2i300000000000000000000000000000000
χ794-4-444-4-2-4440000-4-2-2-2222200000000002-22-2000000002i32i3−2i3−2i3−2i3−2i32i32i300000000000000000000000000000000
χ804-4-44-4444-440000-44-4-444-4-400000000004-4-44000000000000000000000000000000000000000000000000
χ814-4-44-44-24-440000-4-222-2-2220000000000-222-2−2i3−2i32i32i32i32i3−2i3−2i30000000000000000000000000000000000000000
χ824-4-44-44-24-440000-4-222-2-2220000000000-222-22i32i3−2i3−2i3−2i3−2i32i32i30000000000000000000000000000000000000000
χ834-4-44-44-2-44-400004-222-2-2220044-4-400002-2-22-2-222-2-2220000000000000000000000000000000000000000
χ844-4-44-44-2-44-400004-222-2-22200-4-44400002-2-2222-2-222-2-20000000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 24 (ζ24 = 1); i = ζ6.