Finite Group Databasebeta

← Group #10827764

Character table — Group #10827764

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69
size112222222224444444444488888888888888888888121212121212161616161616161616162424242424242424244848
order12222222236224466666662444444466121212121212121212124444444461212121212121222444444444
χ1111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1111111-1-11111-1-1-1-1-1-11-1-11111-1-1
χ4111111111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-111-1-1-1-111
χ51111111111111111111111-1-11111-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-111-1-111
χ61111111111111111111111-1-11111-1-1111111111111-1-11111-1-1-1-1-1-1-1-1-1-111-111-1-111-1-1
χ71111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-111111111111-1-1-1-1
χ81111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-1-1-1-1-1-11111
χ911111111111-1-1-1-111111111111-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-11-111-1-111-1-11-111-1-1-1111-1
χ1011111111111-1-1-1-111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-111111-111-1-111-1-1-11-1-1111-1-1-11
χ1111111111111-1-1-1-1111111111-1-111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1111-1-1-1-111-111-11-1-111-11
χ1211111111111-1-1-1-1111111111-1-111-1-1-1-1-1-1-1-1-1-11111-1-11111-1111-1-1-1-1111-1-11-111-1-11-1
χ1311111111111-1-1-1-11111111-1-111-1-111-1-1-1-11111-1-1-1-1111111-11-1-111-1-111-111-11-1-1-1-11-1
χ1411111111111-1-1-1-11111111-1-111-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-11-1-111-1-1111-1-11-11111-11
χ1511111111111-1-1-1-11111111-1-1-1-11111-1-1-1-1-1-1-1-111111111111-1-1-11111-1-11-111-1-1-1-1-1-11
χ1611111111111-1-1-1-11111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-11-1-1-11111-1-1-11-1-1111111-1
χ17222222222-1-12222-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-100000022-1-1-1-1-1-1-1-100000000000
χ18222222222-1-12222-1-1-1-1-1-1-122-2-2-2-222-1-1-1-111111111000000-2-2-1-1-1-1111100000000000
χ19222222222-1-12222-1-1-1-1-1-1-1-2-22222-2-2-1-1-1-1-1-1-1-1-1-1-1-1000000-2-21111111100000000000
χ20222222222-1-12222-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2-1-1-1-111111111000000221111-1-1-1-100000000000
χ21222222222-1-1-2-2-2-2-1-1-1-1-1-1-12222-2-2-2-21111-1-1-1-111110000002-2-1-111-1-11100000000000
χ22222222222-1-1-2-2-2-2-1-1-1-1-1-1-122-2-222-2-211111111-1-1-1-1000000-22-1-11111-1-100000000000
χ23222222222-1-1-2-2-2-2-1-1-1-1-1-1-1-2-222-2-2221111-1-1-1-11111000000-2211-1-111-1-100000000000
χ24222222222-1-1-2-2-2-2-1-1-1-1-1-1-1-2-2-2-2222211111111-1-1-1-10000002-211-1-1-1-11100000000000
χ252222-2-22-2-222000022-22-2-2-200002i−2i00000000002i2i−2i−2i002i2i−2i−2i0000000000200-20000000
χ262222-2-22-2-222000022-22-2-2-200002i−2i00000000002i2i−2i−2i00−2i−2i2i2i0000000000-20020000000
χ272222-2-22-2-222000022-22-2-2-20000−2i2i0000000000−2i−2i2i2i002i2i−2i−2i0000000000-20020000000
χ282222-2-22-2-222000022-22-2-2-20000−2i2i0000000000−2i−2i2i2i00−2i−2i2i2i0000000000200-20000000
χ29222-22-2-22-22200002-22-22-2-2002i−2i000000002i2i−2i−2i0000002i−2i2i−2i00000000000200-2000000
χ30222-22-2-22-22200002-22-22-2-2002i−2i000000002i2i−2i−2i000000−2i2i−2i2i00000000000-2002000000
χ31222-22-2-22-22200002-22-22-2-200−2i2i00000000−2i−2i2i2i0000002i−2i2i−2i00000000000-2002000000
χ32222-22-2-22-22200002-22-22-2-200−2i2i00000000−2i−2i2i2i000000−2i2i−2i2i00000000000200-2000000
χ33222-2-22-2-222222-2-22-2-2-2-2220000000022-2-200000000002-2-22000000000000000002-200
χ34222-2-22-2-222222-2-22-2-2-2-2220000000022-2-20000000000-222-200000000000000000-2200
χ35222-2-22-2-2222-2-2222-2-2-2-22200000000-2-22200000000002-2-2200000000000000000-2200
χ36222-2-22-2-2222-2-2222-2-2-2-22200000000-2-2220000000000-222-2000000000000000002-200
χ3722-222-2-2-22222-22-2-2-2-2222-2000000002-22-200000000220000000000000000-2002-20000
χ3822-222-2-2-22222-22-2-2-2-2222-2000000002-22-200000000-2-20000000000000000200-220000
χ3922-222-2-2-2222-22-22-2-2-2222-200000000-22-2200000000220000000000000000-200-220000
χ4022-222-2-2-2222-22-22-2-2-2222-200000000-22-2200000000-2-200000000000000002002-20000
χ4122-2-2-2-2222222-2-22-222-2-22-22-200002-22-2-2200000000000000002-22-2000000000000000
χ4222-2-2-2-2222222-2-22-222-2-22-2-220000-222-2-220000000000000000-22-22000000000000000
χ4322-2-2-2-222222-222-2-222-2-22-22-20000-22-222-200000000000000002-2-22000000000000000
χ4422-2-2-2-222222-222-2-222-2-22-2-2200002-2-222-20000000000000000-222-2000000000000000
χ4522-2-2-2-2222-1-12-2-221-1-111-112-200002-2-111-13−33−33−33−300000000-11-113−33−300000000000
χ4622-2-2-2-2222-1-12-2-221-1-111-112-200002-2-111-1−33−33−33−3300000000-11-11−33−3300000000000
χ4722-2-2-2-2222-1-12-2-221-1-111-11-220000-22-111-13−33−33−33−3000000001-11-1−33−3300000000000
χ4822-2-2-2-2222-1-12-2-221-1-111-11-220000-22-111-1−33−33−33−33000000001-11-13−33−300000000000
χ4922-2-2-2-2222-1-1-222-21-1-111-112-20000-221-1-113−33−3−33−3300000000-111-13−3−3300000000000
χ5022-2-2-2-2222-1-1-222-21-1-111-112-20000-221-1-11−33−333−33−300000000-111-1−333−300000000000
χ5122-2-2-2-2222-1-1-222-21-1-111-11-2200002-21-1-113−33−3−33−33000000001-1-11−333−300000000000
χ5222-2-2-2-2222-1-1-222-21-1-111-11-2200002-21-1-11−33−333−33−3000000001-1-113−3−3300000000000
χ534444-4-44-4-4-2-20000-2-22-222200004i−4i0000000000−2i−2i2i2i000000000000000000000000000
χ544444-4-44-4-4-2-20000-2-22-22220000−4i4i00000000002i2i−2i−2i000000000000000000000000000
χ55444-44-4-44-4-2-20000-22-22-222004i−4i00000000−2i−2i2i2i0000000000000000000000000000000
χ56444-44-4-44-4-2-20000-22-22-22200−4i4i000000002i2i−2i−2i0000000000000000000000000000000
χ57444-4-44-4-44-2-244-4-4-22222-2-200000000-2-22200000000000000000000000000000000000
χ58444-4-44-4-44-2-2-4-444-22222-2-20000000022-2-200000000000000000000000000000000000
χ5944-444-4-4-44-2-24-44-4222-2-2-2200000000-22-2200000000000000000000000000000000000
χ6044-444-4-4-44-2-2-44-44222-2-2-22000000002-22-200000000000000000000000000000000000
χ6144-44-44-44-4440000-4-444-4-4400000000000000000000000000000000000000000000000
χ6244-44-44-44-4-2-2000022-2-222-2000000000000−2i32i32i3−2i30000000000000000000000000000000
χ6344-44-44-44-4-2-2000022-2-222-20000000000002i3−2i3−2i32i30000000000000000000000000000000
χ6444-4-4444-4-4440000-44-4-44-4400000000000000000000000000000000000000000000000
χ6544-4-4444-4-4-2-200002-222-22-20000000000000000−2i32i32i3−2i3000000000000000000000000000
χ6644-4-4444-4-4-2-200002-222-22-200000000000000002i3−2i3−2i32i3000000000000000000000000000
χ678-800000008-800000000000000000000000000000004i−4i0000000000000000000000000
χ688-800000008-80000000000000000000000000000000−4i4i0000000000000000000000000
χ6916-160000000-880000000000000000000000000000000000000000000000000000000000

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