Finite Group Databasebeta

← Group #10591120

Character table — Group #10591120

Order 576.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84
size11111111222222222222222222224444444444444444444444441212121212121212121212121212121212121212121212121818181818181818
order122244442233446666661212121212121212366666666666121212121212121212121212888888882424242424242424242424242424242444444444
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ41111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ511111111-1-111-1-1111111111111111-1-1-1-111-1-1-1-11-1-1-1-11111-1-1-1-111-1-111-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1
χ611111111-1-111-1-1111111111111111-1-1-1-111-1-1-1-11-1-1-1-11111-1-1-1-111-1-1-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-11111
χ711111111-1-111-1-1111111111111111-1-1-1-111-1-1-1-11-1-1-1-11111-1-1-1-1-1-11111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111
χ811111111-1-111-1-1111111111111111-1-1-1-111-1-1-1-11-1-1-1-11111-1-1-1-1-1-111-1-111-1-1-1-11111-1-1-1-111111111-1-1-1-1
χ91111-1-1-1-11111-1-1111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1i−ii−ii−ii−iii−i−iii−i−iii−i−iii−i−i11-1-111-1-1
χ101111-1-1-1-11111-1-1111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1i−ii−i−ii−iiii−i−iii−i−i−i−iii−i−iii-1-111-1-111
χ111111-1-1-1-11111-1-1111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1−ii−iii−ii−i−i−iii−i−iiiii−i−iii−i−i-1-111-1-111
χ121111-1-1-1-11111-1-1111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1−ii−ii−ii−ii−i−iii−i−iii−i−iii−i−iii11-1-111-1-1
χ131111-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-11-1-1-1-111-1-1-1-111111-1-1-1-11111i−i−iii−i−iiii−i−i−i−iiiii−i−i−i−iii11-1-1-1-111
χ141111-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-11-1-1-1-111-1-1-1-111111-1-1-1-11111i−i−ii−iii−iii−i−i−i−iii−i−iiiii−i−i-1-11111-1-1
χ151111-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-11-1-1-1-111-1-1-1-111111-1-1-1-11111−iii−ii−i−ii−i−iiiii−i−iii−i−i−i−iii-1-11111-1-1
χ161111-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-11-1-1-1-111-1-1-1-111111-1-1-1-11111−iii−i−iii−i−i−iiiii−i−i−i−iiiii−i−i11-1-1-1-111
χ1722222222222-12222-1-12-122-1-122-1-1-122-1-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-1-1-10000222200000000-1-1-1-1-1-1-1-100000000
χ1822222222222-12222-1-12-122-1-122-1-1-122-1-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-1-1-10000-2-2-2-2000000001111111100000000
χ192222222222-1222-1-122-12-1-122-1-122-1-1-122-1-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-122220000-1-1-1-1-1-1-1-10000000000000000
χ202222222222-1222-1-122-12-1-122-1-122-1-1-122-1-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-1-2-2-2-20000111111110000000000000000
χ2122222222-2-22-1-2-222-1-12-122-1-122-1-1-1-2-211-1-11111-1-2-211-1-1-1-11111000022-2-200000000-1-1-1-1111100000000
χ2222222222-2-22-1-2-222-1-12-122-1-122-1-1-1-2-211-1-11111-1-2-211-1-1-1-111110000-2-222000000001111-1-1-1-100000000
χ2322222222-2-2-12-2-2-1-122-12-1-122-1-122-111-2-2-1-11111-111-2-2-1-1-1-1111122-2-20000-1-1-1-111110000000000000000
χ2422222222-2-2-12-2-2-1-122-12-1-122-1-122-111-2-2-1-11111-111-2-2-1-1-1-11111-2-22200001111-1-1-1-10000000000000000
χ252222-2-2-2-2222-1-2-222-1-12-1-2-211-2-211-122-1-1-1-1-1-1-1-1-1-2-2111111111100002i−2i2i−2i00000000−i−iii−i−iii00000000
χ262222-2-2-2-2222-1-2-222-1-12-1-2-211-2-211-122-1-1-1-1-1-1-1-1-1-2-211111111110000−2i2i−2i2i00000000ii−i−iii−i−i00000000
χ272222-2-2-2-222-12-2-2-1-122-1211-2-211-2-2-1-1-122-1-1-1-1-1-1-111-2-2111111112i−2i2i−2i0000−i−iii−i−iii0000000000000000
χ282222-2-2-2-222-12-2-2-1-122-1211-2-211-2-2-1-1-122-1-1-1-1-1-1-111-2-211111111−2i2i−2i2i0000ii−i−iii−i−i0000000000000000
χ292222-2-2-2-2-2-22-12222-1-12-1-2-211-2-211-1-2-211-1-11111-122-1-11111-1-1-1-100002i−2i−2i2i00000000−i−iiiii−i−i00000000
χ302222-2-2-2-2-2-22-12222-1-12-1-2-211-2-211-1-2-211-1-11111-122-1-11111-1-1-1-10000−2i2i2i−2i00000000ii−i−i−i−iii00000000
χ312222-2-2-2-2-2-2-1222-1-122-1211-2-211-2-2-111-2-2-1-11111-1-1-1221111-1-1-1-12i−2i−2i2i0000−i−iiiii−i−i0000000000000000
χ322222-2-2-2-2-2-2-1222-1-122-1211-2-211-2-2-111-2-2-1-11111-1-1-1221111-1-1-1-1−2i2i2i−2i0000ii−i−i−i−iii0000000000000000
χ3322-2-222-2-22-2222-2-2-2-2-2222222-2-2-2-222-22-2-2-222-2-222-22-222-2-222-2-200000000000000000000000000000000
χ3422-2-222-2-22-22-12-2-2-2112-122-1-1-2-211-12-2-1111-1-111-12-2-11-1-111-1-11100000000000000003−33−33−33−300000000
χ3522-2-222-2-22-22-12-2-2-2112-122-1-1-2-211-12-2-1111-1-111-12-2-11-1-111-1-1110000000000000000−33−33−33−3300000000
χ3622-2-222-2-22-2-122-211-2-2-12-1-12211-2-2-1-112-211-1-111-1-112-2-1-111-1-111000000003−33−33−33−30000000000000000
χ3722-2-222-2-22-2-122-211-2-2-12-1-12211-2-2-1-112-211-1-111-1-112-2-1-111-1-11100000000−33−33−33−330000000000000000
χ3822-2-222-2-2-2222-22-2-2-2-2222222-2-2-2-22-22-22-2-2-2-2222-22-2222-2-2-2-22200000000000000000000000000000000
χ3922-2-222-2-2-222-1-22-2-2112-122-1-1-2-211-1-221-11111-1-1-1-221-1-1-11111-1-100000000000000003−33−3−33−3300000000
χ4022-2-222-2-2-222-1-22-2-2112-122-1-1-2-211-1-221-11111-1-1-1-221-1-1-11111-1-10000000000000000−33−333−33−300000000
χ4122-2-222-2-2-22-12-2211-2-2-12-1-12211-2-2-11-1-221111-1-1-11-1-22-1-11111-1-1000000003−33−3−33−330000000000000000
χ4222-2-222-2-2-22-12-2211-2-2-12-1-12211-2-2-11-1-221111-1-1-11-1-22-1-11111-1-100000000−33−333−33−30000000000000000
χ4322-2-2-2-2222-222-22-2-2-2-222-2-2-2-2222222-22-2-2-222-2-22-22-22-2-222-2-22200000000000000000000000000000000
χ4422-2-2-2-2222-22-1-22-2-2112-1-2-21122-1-1-12-2-1111-1-111-1-221-111-1-111-1-10000000000000000−i3i3i3−i3−i3i3i3−i300000000
χ4522-2-2-2-2222-22-1-22-2-2112-1-2-21122-1-1-12-2-1111-1-111-1-221-111-1-111-1-10000000000000000i3−i3−i3i3i3−i3−i3i300000000
χ4622-2-2-2-2222-2-12-2211-2-2-1211-2-2-1-122-1-112-211-1-111-11-1-2211-1-111-1-100000000−i3i3i3−i3−i3i3i3−i30000000000000000
χ4722-2-2-2-2222-2-12-2211-2-2-1211-2-2-1-122-1-112-211-1-111-11-1-2211-1-111-1-100000000i3−i3−i3i3i3−i3−i3i30000000000000000
χ4822-2-2-2-222-22222-2-2-2-2-222-2-2-2-222222-22-22-2-2-2-22222-22-2-2-22222-2-200000000000000000000000000000000
χ4922-2-2-2-222-222-12-2-2-2112-1-2-21122-1-1-1-221-11111-1-1-12-2-1111-1-1-1-1110000000000000000−i3i3i3−i3i3−i3−i3i300000000
χ5022-2-2-2-222-222-12-2-2-2112-1-2-21122-1-1-1-221-11111-1-1-12-2-1111-1-1-1-1110000000000000000i3−i3−i3i3−i3i3i3−i300000000
χ5122-2-2-2-222-22-122-211-2-2-1211-2-2-1-122-11-1-221111-1-1-1-112-211-1-1-1-11100000000−i3i3i3−i3i3−i3−i3i30000000000000000
χ5222-2-2-2-222-22-122-211-2-2-1211-2-2-1-122-11-1-221111-1-1-1-112-211-1-1-1-11100000000i3−i3−i3i3−i3i3i3−i30000000000000000
χ532-22-22i−2i2i−2i0022002-22-2-2-22i−2i2i−2i2i−2i2i−2i200002-20000-200002i−2i2i−2i000000000000000000000000000000002i−2i2-2
χ542-22-22i−2i2i−2i0022002-22-2-2-22i−2i2i−2i2i−2i2i−2i200002-20000-200002i−2i2i−2i00000000000000000000000000000000−2i2i-22
χ552-22-2−2i2i−2i2i0022002-22-2-2-2−2i2i−2i2i−2i2i−2i2i200002-20000-20000−2i2i−2i2i000000000000000000000000000000002i−2i-22
χ562-22-2−2i2i−2i2i0022002-22-2-2-2−2i2i−2i2i−2i2i−2i2i200002-20000-20000−2i2i−2i2i00000000000000000000000000000000−2i2i2-2
χ572-2-222i−2i−2i2i002200-22-22-2-22i−2i2i−2i−2i2i−2i2i20000-220000-200002i−2i−2i2i00000000000000000000000000002-22i−2i0000
χ582-2-222i−2i−2i2i002200-22-22-2-22i−2i2i−2i−2i2i−2i2i20000-220000-200002i−2i−2i2i0000000000000000000000000000-22−2i2i0000
χ592-2-22−2i2i2i−2i002200-22-22-2-2−2i2i−2i2i2i−2i2i−2i20000-220000-20000−2i2i2i−2i00000000000000000000000000002-2−2i2i0000
χ602-2-22−2i2i2i−2i002200-22-22-2-2−2i2i−2i2i2i−2i2i−2i20000-220000-20000−2i2i2i−2i0000000000000000000000000000-222i−2i0000
χ614444444444-2-244-2-2-2-2-2-2-2-2-2-2-2-2-2-21-2-2-2-21111111-2-2-2-21111111100000000000000000000000000000000
χ6244444444-4-4-2-2-4-4-2-2-2-2-2-2-2-2-2-2-2-2-2-21222211-1-1-1-1122221111-1-1-1-100000000000000000000000000000000
χ634444-4-4-4-444-2-2-4-4-2-2-2-2-2-2222222221-2-2-2-211111112222-1-1-1-1-1-1-1-100000000000000000000000000000000
χ644444-4-4-4-4-4-4-2-244-2-2-2-2-2-2222222221222211-1-1-1-11-2-2-2-2-1-1-1-1111100000000000000000000000000000000
χ6544-4-444-4-44-4-2-24-42222-2-2-2-2-2-222221-22-22-1-111-1-11-22-2211-1-111-1-100000000000000000000000000000000
χ6644-4-444-4-4-44-2-2-442222-2-2-2-2-2-2222212-22-2-1-1-1-11112-22-211-1-1-1-11100000000000000000000000000000000
χ6744-4-4-4-4444-4-2-2-442222-2-22222-2-2-2-21-22-22-1-111-1-112-22-2-1-111-1-11100000000000000000000000000000000
χ6844-4-4-4-444-44-2-24-42222-2-22222-2-2-2-212-22-2-1-1-1-1111-22-22-1-11111-1-100000000000000000000000000000000
χ694-44-44i−4i4i−4i004-2004-4-22-424i−4i−2i2i4i−4i−2i2i-20000-22000020000−2i2i−2i2i000000000000000000000000000000000000
χ704-44-44i−4i4i−4i00-2400-224-42-4−2i2i4i−4i−2i2i4i−4i-20000-22000020000−2i2i−2i2i000000000000000000000000000000000000
χ714-44-44i−4i4i−4i00-2-200-22-2222−2i2i−2i2i−2i2i−2i2i100001-13-33-3-10000i−ii−i3i−3i3i−3i00000000000000000000000000000000
χ724-44-44i−4i4i−4i00-2-200-22-2222−2i2i−2i2i−2i2i−2i2i100001-1-33-33-10000i−ii−i−3i3i−3i3i00000000000000000000000000000000
χ734-44-4−4i4i−4i4i004-2004-4-22-42−4i4i2i−2i−4i4i2i−2i-20000-220000200002i−2i2i−2i000000000000000000000000000000000000
χ744-44-4−4i4i−4i4i00-2400-224-42-42i−2i−4i4i2i−2i−4i4i-20000-220000200002i−2i2i−2i000000000000000000000000000000000000
χ754-44-4−4i4i−4i4i00-2-200-22-22222i−2i2i−2i2i−2i2i−2i100001-13-33-3-10000−ii−ii−3i3i−3i3i00000000000000000000000000000000
χ764-44-4−4i4i−4i4i00-2-200-22-22222i−2i2i−2i2i−2i2i−2i100001-1-33-33-10000−ii−ii3i−3i3i−3i00000000000000000000000000000000
χ774-4-444i−4i−4i4i004-200-442-2-424i−4i−2i2i−4i4i2i−2i-200002-2000020000−2i2i2i−2i000000000000000000000000000000000000
χ784-4-444i−4i−4i4i00-24002-2-442-4−2i2i4i−4i2i−2i−4i4i-200002-2000020000−2i2i2i−2i000000000000000000000000000000000000
χ794-4-444i−4i−4i4i00-2-2002-22-222−2i2i−2i2i2i−2i2i−2i10000-113-3-33-10000i−i−ii3i−3i−3i3i00000000000000000000000000000000
χ804-4-444i−4i−4i4i00-2-2002-22-222−2i2i−2i2i2i−2i2i−2i10000-11-333-3-10000i−i−ii−3i3i3i−3i00000000000000000000000000000000
χ814-4-44−4i4i4i−4i004-200-442-2-42−4i4i2i−2i4i−4i−2i2i-200002-20000200002i−2i−2i2i000000000000000000000000000000000000
χ824-4-44−4i4i4i−4i00-24002-2-442-42i−2i−4i4i−2i2i4i−4i-200002-20000200002i−2i−2i2i000000000000000000000000000000000000
χ834-4-44−4i4i4i−4i00-2-2002-22-2222i−2i2i−2i−2i2i−2i2i10000-113-3-33-10000−iii−i−3i3i3i−3i00000000000000000000000000000000
χ844-4-44−4i4i4i−4i00-2-2002-22-2222i−2i2i−2i−2i2i−2i2i10000-11-333-3-10000−iii−i3i−3i−3i3i00000000000000000000000000000000

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