Finite Group Databasebeta

← Group #10828670

Character table — Group #10828670

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72
size1111222222222244444444444444444488888888888816161616161616161616161624242424242424242424242424242424
order122222344446662244444466121212121212121244661212121212121212888824242424242424242244444444444444
χ1111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ411111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ5111111111111111111-1-1-1-11111111111-1-111-1-1-1-1-1-1-1-111-1-11111-1-1-1-11-111-1-11-11111-1-1-1-1
χ6111111111111111111-1-1-1-11111111111-1-111-1-1-1-1-1-1-1-111-1-11111-1-1-1-1-11-1-111-11-1-1-1-11111
χ7111111111111111111-1-1-1-11111111111-1-111-1-1-1-1-1-1-1-1-1-111-1-1-1-111111-111-1-11-1-1-1-1-11111
χ8111111111111111111-1-1-1-11111111111-1-111-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-11-1-111-111111-1-1-1-1
χ911111111111111-1-1-1-1111111-1-1-1-11111-1-1-1-11111-1-1-1-11-11-111-1-111-1-11-11-11-1-1111-1-111-1-1
χ1011111111111111-1-1-1-1111111-1-1-1-11111-1-1-1-11111-1-1-1-11-11-111-1-111-1-1-11-11-111-1-1-111-1-111
χ1111111111111111-1-1-1-1111111-1-1-1-11111-1-1-1-11111-1-1-1-1-11-11-1-111-1-1111-11-11-1-11-1-111-1-111
χ1211111111111111-1-1-1-1111111-1-1-1-11111-1-1-1-11111-1-1-1-1-11-11-1-111-1-111-11-11-111-111-1-111-1-1
χ1311111111111111-1-1-1-1-1-1-1-111-1-1-1-1111111-1-1-1-1-1-111111-1-1111-1-1-1-111111-1-11-1-111-1-1-1-111
χ1411111111111111-1-1-1-1-1-1-1-111-1-1-1-1111111-1-1-1-1-1-111111-1-1111-1-1-1-111-1-1-111-111-1-11111-1-1
χ1511111111111111-1-1-1-1-1-1-1-111-1-1-1-1111111-1-1-1-1-1-11111-111-1-1-11111-1-1111-1-11-1-1-1-11111-1-1
χ1611111111111111-1-1-1-1-1-1-1-111-1-1-1-1111111-1-1-1-1-1-11111-111-1-1-11111-1-1-1-1-111-11111-1-1-1-111
χ172222222-2-2-2-222222-2-222-2-222-2-2-2-2-2-2-2-22-22222-2-222-2-20000000000000000000000000000
χ182222222-2-2-2-222222-2-2-2-22222-2-2-2-2-2-2-2-2-2222-2-222-2-2220000000000000000000000000000
χ192222222-2-2-2-2222-2-22222-2-2222222-2-2-2-2-22-2-222-2-2-2-2220000000000000000000000000000
χ202222222-2-2-2-2222-2-222-2-222222222-2-2-2-22-2-2-2-2-22222-2-20000000000000000000000000000
χ21222222-12222-1-1-122222222-1-1-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-10000000000000000
χ22222222-12222-1-1-122222222-1-1-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-1-1-1-2-2-2-2111111110000000000000000
χ23222222-12222-1-1-12222-2-2-2-2-1-1-1-1-1-1-1-1-1-1-2-2-1-11111111122-2-2-1-1-1-111110000000000000000
χ24222222-12222-1-1-12222-2-2-2-2-1-1-1-1-1-1-1-1-1-1-2-2-1-111111111-2-2221111-1-1-1-10000000000000000
χ25222222-12222-1-1-1-2-2-2-22222-1-11111-1-1-1-1-2-211-1-1-1-111112-22-2-1-111-1-1110000000000000000
χ26222222-12222-1-1-1-2-2-2-22222-1-11111-1-1-1-1-2-211-1-1-1-11111-22-2211-1-111-1-10000000000000000
χ27222222-12222-1-1-1-2-2-2-2-2-2-2-2-1-11111-1-1-1-122111111-1-1-1-12-2-22-1-11111-1-10000000000000000
χ28222222-12222-1-1-1-2-2-2-2-2-2-2-2-1-11111-1-1-1-122111111-1-1-1-1-222-211-1-1-1-1110000000000000000
χ29222222-1-2-2-2-2-1-1-122-2-222-2-2-1-1111111112-2-1-1-1-111-1-11100003−33−33−33−30000000000000000
χ30222222-1-2-2-2-2-1-1-122-2-222-2-2-1-1111111112-2-1-1-1-111-1-1110000−33−33−33−330000000000000000
χ31222222-1-2-2-2-2-1-1-122-2-2-2-222-1-111111111-22-1-111-1-111-1-100003−33−3−33−330000000000000000
χ32222222-1-2-2-2-2-1-1-122-2-2-2-222-1-111111111-22-1-111-1-111-1-10000−33−333−33−30000000000000000
χ33222222-1-2-2-2-2-1-1-1-2-22222-2-2-1-1-1-1-1-11111-2211-1-11111-1-100003−3−333−3−330000000000000000
χ34222222-1-2-2-2-2-1-1-1-2-22222-2-2-1-1-1-1-1-11111-2211-1-11111-1-10000−333−3−333−30000000000000000
χ35222222-1-2-2-2-2-1-1-1-2-222-2-222-1-1-1-1-1-111112-21111-1-1-1-11100003−3−33−333−30000000000000000
χ36222222-1-2-2-2-2-1-1-1-2-222-2-222-1-1-1-1-1-111112-21111-1-1-1-1110000−333−33−3−330000000000000000
χ372222-2-2222-2-22222-22-20000-2-222-2-222-2-2002-20000000000000000000020-2200-2000000000
χ382222-2-2222-2-22222-22-20000-2-222-2-222-2-2002-200000000000000000000-202-2002000000000
χ392222-2-2222-2-2222-22-220000-2-2-2-22222-2-200-220000000000000000000020-2-2002000000000
χ402222-2-2222-2-2222-22-220000-2-2-2-22222-2-200-2200000000000000000000-202200-2000000000
χ412222-2-22-2-2222222-2-220000-2-2-2-222-2-222002-2000000000000000000000200-2-20200000000
χ422222-2-22-2-2222222-2-220000-2-2-2-222-2-222002-2000000000000000000000-200220-200000000
χ432222-2-22-2-222222-222-20000-2-222-2-2-2-22200-220000000000000000000002002-20-200000000
χ442222-2-22-2-222222-222-20000-2-222-2-2-2-22200-22000000000000000000000-200-220200000000
χ4522-2-2-2222-22-22-2-200002i−2i2i−2i2-200002-22-200002i−2i2i−2i000000000000000000000000002i−2i002-2
χ4622-2-2-2222-22-22-2-200002i−2i2i−2i2-200002-22-200002i−2i2i−2i00000000000000000000000000−2i2i00-22
χ4722-2-2-2222-22-22-2-20000−2i2i−2i2i2-200002-22-20000−2i2i−2i2i000000000000000000000000002i−2i00-22
χ4822-2-2-2222-22-22-2-20000−2i2i−2i2i2-200002-22-20000−2i2i−2i2i00000000000000000000000000−2i2i002-2
χ4922-2-2-222-22-222-2-200002i−2i−2i2i2-20000-22-2200002i−2i−2i2i0000000000000000000000002i−2i002-200
χ5022-2-2-222-22-222-2-200002i−2i−2i2i2-20000-22-2200002i−2i−2i2i000000000000000000000000−2i2i00-2200
χ5122-2-2-222-22-222-2-20000−2i2i2i−2i2-20000-22-220000−2i2i2i−2i0000000000000000000000002i−2i00-2200
χ5222-2-2-222-22-222-2-20000−2i2i2i−2i2-20000-22-220000−2i2i2i−2i000000000000000000000000−2i2i002-200
χ534444-4-4-244-4-4-2-2-24-44-4000022-2-222-2-22200-22000000000000000000000000000000000000
χ544444-4-4-244-4-4-2-2-2-44-4400002222-2-2-2-222002-2000000000000000000000000000000000000
χ554444-4-4-2-4-444-2-2-24-4-4400002222-2-222-2-200-22000000000000000000000000000000000000
χ564444-4-4-2-4-444-2-2-2-444-4000022-2-22222-2-2002-2000000000000000000000000000000000000
χ5744-4-44-444-4-444-4-400000000-4400004-4-440000000000000000000000000000000000000000
χ5844-4-44-44-444-44-4-400000000-440000-444-40000000000000000000000000000000000000000
χ5944-4-44-4-24-4-44-222000000002-20000-222-20000000023−2323−230000000000000000000000000000
χ6044-4-44-4-24-4-44-222000000002-20000-222-200000000−2323−23230000000000000000000000000000
χ6144-4-44-4-2-444-4-222000000002-200002-2-220000000023−23−23230000000000000000000000000000
χ6244-4-44-4-2-444-4-222000000002-200002-2-2200000000−232323−230000000000000000000000000000
χ6344-4-4-44-24-44-4-22200004i−4i4i−4i-220000-22-220000−2i2i−2i2i00000000000000000000000000000000
χ6444-4-4-44-24-44-4-2220000−4i4i−4i4i-220000-22-2200002i−2i2i−2i00000000000000000000000000000000
χ6544-4-4-44-2-44-44-22200004i−4i−4i4i-2200002-22-20000−2i2i2i−2i00000000000000000000000000000000
χ6644-4-4-44-2-44-44-2220000−4i4i4i−4i-2200002-22-200002i−2i−2i2i00000000000000000000000000000000
χ678-88-80080000-88-80000000000000000000000000000000000000000000000000000000000
χ688-88-800-400004-44000000000043−430000000000000000000000000000000000000000000000
χ698-88-800-400004-440000000000−43430000000000000000000000000000000000000000000000
χ708-8-880080000-8-880000000000000000000000000000000000000000000000000000000000
χ718-8-8800-4000044-400000000000043−4300000000000000000000000000000000000000000000
χ728-8-8800-4000044-4000000000000−434300000000000000000000000000000000000000000000

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