Finite Group Databasebeta

← Group #10849658

Character table — Group #10849658

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72
size11112222222222444444444444448888888888888888881212121216161616161616161616242424242424242424244848
order1222223444466644446612121212121212122222888812122424242424242424444466668824242424244444444444
χ1111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1111111-1-1-1-1-1-1
χ411111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111111
χ51111111111111111111111111111-1-1-1-1111111111111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1
χ61111111111111111111111111111-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111
χ71111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-111
χ81111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-111111111-1-1
χ911111111111111-1-1-1-1111-1-1-1-111111-1-111-1-1-1-11111-1-1-1-1111111-1-11-111-1-1-1-111-1-111-1-11-1
χ1011111111111111-1-1-1-1111-1-1-1-111111-1-111-1-1-1-11111-1-1-1-1-1-1-1-111-1-11-111-1-111-1-111-1-111-11
χ1111111111111111-1-1-1-1111-1-1-1-111111-1-1-1-111-1-1-1-1-1-11111111111-1-1-11-1-111-1-111-1-1-1-111-11
χ1211111111111111-1-1-1-1111-1-1-1-111111-1-1-1-111-1-1-1-1-1-11111-1-1-1-111-1-1-11-1-11111-1-11111-1-11-1
χ1311111111111111-1-1-1-1111-1-1-1-1111-1-11111-1-1-1-11111-1-1-1-11111-1-111-11-1-111-1-1-1-11111-1-1-11
χ1411111111111111-1-1-1-1111-1-1-1-1111-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-111-11-1-1111111-1-1-1-1111-1
χ1511111111111111-1-1-1-1111-1-1-1-1111-1-111-1-111-1-1-1-1-1-111111111-1-1111-111-1-1-1-1-1-111-1-1111-1
χ1611111111111111-1-1-1-1111-1-1-1-1111-1-111-1-111-1-1-1-1-1-11111-1-1-1-1-1-1111-111-1-11111-1-111-1-1-11
χ172222222-2-2-2-222222-2-222-222-2-2-2-2-22-22-200002-20000000000002-22-2000000000000000000
χ182222222-2-2-2-222222-2-222-222-2-2-2-2-2-22-2200002-2000000000000-22-22000000000000000000
χ192222222-2-2-2-2222-2-22222-2-2-222-2-2-22-2-220000-220000000000002-2-22000000000000000000
χ202222222-2-2-2-2222-2-22222-2-2-222-2-2-2-222-20000-22000000000000-222-2000000000000000000
χ21222222-12222-1-1-12222-1-1-1-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-10000-1-1-1-122-1-1-1-1000000000000
χ22222222-12222-1-1-12222-1-1-1-1-1-1-1-1-1-12222-2-2-2-2-1-1111111110000-1-1-1-1-2-21111000000000000
χ23222222-12222-1-1-12222-1-1-1-1-1-1-1-1-1-1-2-2-2-22222-1-1-1-1-1-1-1-1-1-100001111-2-21111000000000000
χ24222222-12222-1-1-12222-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2-1-1111111110000111122-1-1-1-1000000000000
χ25222222-12222-1-1-1-2-2-2-2-1-1-11111-1-1-122-2-222-2-211-1-1-1-111110000-1-1112-2-1-111000000000000
χ26222222-12222-1-1-1-2-2-2-2-1-1-11111-1-1-122-2-2-2-222111111-1-1-1-10000-1-111-2211-1-1000000000000
χ27222222-12222-1-1-1-2-2-2-2-1-1-11111-1-1-1-2-22222-2-211-1-1-1-11111000011-1-1-2211-1-1000000000000
χ28222222-12222-1-1-1-2-2-2-2-1-1-11111-1-1-1-2-222-2-222111111-1-1-1-1000011-1-12-2-1-111000000000000
χ29222222-1-2-2-2-2-1-1-122-2-2-1-11-1-1111112-22-20000-1133−3−333−3−30000-11-11003−33−3000000000000
χ30222222-1-2-2-2-2-1-1-122-2-2-1-11-1-1111112-22-20000-11−3−333−3−3330000-11-1100−33−33000000000000
χ31222222-1-2-2-2-2-1-1-122-2-2-1-11-1-111111-22-220000-1133−3−333−3−300001-11-100−33−33000000000000
χ32222222-1-2-2-2-2-1-1-122-2-2-1-11-1-111111-22-220000-11−3−333−3−33300001-11-1003−33−3000000000000
χ33222222-1-2-2-2-2-1-1-1-2-222-1-1111-1-11112-2-2200001-133−3−3−3−3330000-111-1003−3−33000000000000
χ34222222-1-2-2-2-2-1-1-1-2-222-1-1111-1-11112-2-2200001-1−3−33333−3−30000-111-100−333−3000000000000
χ35222222-1-2-2-2-2-1-1-1-2-222-1-1111-1-1111-222-200001-133−3−3−3−33300001-1-1100−333−3000000000000
χ36222222-1-2-2-2-2-1-1-1-2-222-1-1111-1-1111-222-200001-1−3−33333−3−300001-1-11003−3−33000000000000
χ372222-2-222-2-222222-22-2-2-2222-2-2-2-2200000000-220000000022-2-200000000002-20000000000
χ382222-2-222-2-222222-22-2-2-2222-2-2-2-2200000000-2200000000-2-2220000000000-220000000000
χ392222-2-222-2-22222-22-22-2-22-2-222-2-22000000002-20000000022-2-20000000000-220000000000
χ402222-2-222-2-22222-22-22-2-22-2-222-2-22000000002-200000000-2-22200000000002-20000000000
χ412222-2-22-222-22222-2-22-2-2-2222222-200000000-2-20000000000000000000000002-22-2000000
χ422222-2-22-222-22222-2-22-2-2-2222222-200000000-2-2000000000000000000000000-22-22000000
χ432222-2-22-222-2222-222-2-2-2-2-2-2-2-222-200000000220000000000000000000000002-2-22000000
χ442222-2-22-222-2222-222-2-2-2-2-2-2-2-222-20000000022000000000000000000000000-222-2000000
χ4522-2-22-22-22-222-2-200002-2-200002-220000002-20000002-22-22i−2i2i−2i0000000000000000002i−2i00
χ4622-2-22-22-22-222-2-200002-2-200002-220000002-20000002-22-2−2i2i−2i2i000000000000000000−2i2i00
χ4722-2-22-22-22-222-2-200002-2-200002-22000000-22000000-22-222i−2i2i−2i000000000000000000−2i2i00
χ4822-2-22-22-22-222-2-200002-2-200002-22000000-22000000-22-22−2i2i−2i2i0000000000000000002i−2i00
χ4922-2-2-222-2-2222-2-20000-22-20000-22200002-200002-22-200002i−2i−2i2i00000000000000002i−2i0000
χ5022-2-2-222-2-2222-2-20000-22-20000-22200002-200002-22-20000−2i2i2i−2i0000000000000000−2i2i0000
χ5122-2-2-222-2-2222-2-20000-22-20000-2220000-220000-22-2200002i−2i−2i2i0000000000000000−2i2i0000
χ5222-2-2-222-2-2222-2-20000-22-20000-2220000-220000-22-220000−2i2i2i−2i00000000000000002i−2i0000
χ534444-4-4-24-4-44-2-2-24-44-422-2-2-22222-2000000002-20000000000000000000000000000000000
χ544444-4-4-24-4-44-2-2-2-44-4422-222-2-222-200000000-220000000000000000000000000000000000
χ554444-4-4-2-444-4-2-2-24-4-44222-2-2-2-2-2-2200000000220000000000000000000000000000000000
χ564444-4-4-2-444-4-2-2-2-444-42222222-2-2200000000-2-20000000000000000000000000000000000
χ5744-4-44-444-44-44-4-400004-440000-44-400000000000000000000000000000000000000000000
χ5844-4-44-4-24-44-4-2220000-22-200002-220000000000000023−23−232300000000000000000000000000
χ5944-4-44-4-24-44-4-2220000-22-200002-2200000000000000−232323−2300000000000000000000000000
χ6044-4-44-4-2-44-44-2220000-2220000-22-20000004-4000000-22-2200000000000000000000000000
χ6144-4-44-4-2-44-44-2220000-2220000-22-2000000-440000002-22-200000000000000000000000000
χ6244-4-4-44444-4-44-4-40000-44400004-4-400000000000000000000000000000000000000000000
χ6344-4-4-44-244-4-4-22200002-2-20000-222000000000023−23−2323000000000000000000000000000000
χ6444-4-4-44-244-4-4-22200002-2-20000-2220000000000−232323−23000000000000000000000000000000
χ6544-4-4-44-2-4-444-22200002-2200002-2-200004-40000-22-22000000000000000000000000000000
χ6644-4-4-44-2-4-444-22200002-2200002-2-20000-4400002-22-2000000000000000000000000000000
χ678-88-80080000-88-80000000000000000000000000000000000000000000000000000000000
χ688-88-800-400004-440000000−4i34i30000000000000000000000000000000000000000000000000
χ698-88-800-400004-4400000004i3−4i30000000000000000000000000000000000000000000000000
χ708-8-880080000-8-880000000000000000000000000000000000000000000000000000000000
χ718-8-8800-4000044-4000000000−4i34i300000000000000000000000000000000000000000000000
χ728-8-8800-4000044-40000000004i3−4i300000000000000000000000000000000000000000000000

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