Finite Group Databasebeta

← Group #13165690

Character table — Group #13165690

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75
size1111222244444444668888888812121212121212121212181824242424242424242424242424242424243636363636363636363636363636727272108108108
order1222366633666666443366666644121212121212121244266666666121212121212121244881212121212122424242441212288
χ1111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111-1-1-1-1-1-1-1-1-11111111111-1-1111111-1-1-1-1-1-1-11-1-1
χ311111111111111111111111111-1-11111-1-1-1-111111111111-1-111-1-1-1-1-1-1-1-11-1-1-1-11-1-1-1-11111-1-1
χ411111111111111111111111111-1-11111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1111-1-1-1-111111-1-1-1111
χ51111111111111111-1-11111111111-1-1-1-111111111111111111-1-11111-1-1111-1-1-1-111111-1-1-1-1-1-1
χ61111111111111111-1-11111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-11-1-1-1-11-1-1-1-1111-111
χ71111111111111111-1-111111111-1-1-1-1-1-1-1-1-1-111111111111-1-1-1-1-1-1-1-111-1-1111111-1-1-1-1-1-1-1-111
χ81111111111111111-1-111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111111-1-1-1
χ9222222222222222222222222220022220000-2-2000000000002200000000-20000-20000000-200
χ102222222222222222-2-22222222200-2-2-2-20000-2-200000000000-2-200000000-20000-20000000200
χ112222-1-1-1-12222222200-1-1-1-1-1-1-1-12200002222222-1-122-1-1-1-1-1-100-1-1-1-10022-10000-1-1-1-1-1000000
χ122222-1-1-1-12222222200-1-1-1-1-1-1-1-1220000222222-211-2-21111-1-100-1-1-1-100-2-2-10000-11111000000
χ132222-1-1-1-12222222200-1-1-1-1-1-1-1-1-2-20000-2-2-2-2222-1-122-1-1-1-11100111100-2-2-10000-11111000000
χ142222-1-1-1-12222222200-1-1-1-1-1-1-1-1-2-20000-2-2-2-222-211-2-21111110011110022-10000-1-1-1-1-1000000
χ1522-2-22-2-2222-22-22-2-200222-22-2-2-200000000002-2000000000000000002i−2i00-22i2i−2i−2i20000000000
χ1622-2-22-2-2222-22-22-2-200222-22-2-2-200000000002-200000000000000000−2i2i00-2−2i−2i2i2i20000000000
χ1722-2-22-2-2222-22-22-2-200222-22-2-2-22i−2i00002i2i−2i−2i-220000000002i−2i002i2i−2i−2i000020000-20000000000
χ1822-2-22-2-2222-22-22-2-200222-22-2-2-2−2i2i0000−2i−2i2i2i-22000000000−2i2i00−2i−2i2i2i000020000-20000000000
χ1922-2-2-111-122-22-22-2-200-1-1-11-11112i−2i00002i2i−2i−2i-220−i3i300−i3−i3i3i3−ii00−i−iii0000-10000133−3−3000000
χ2022-2-2-111-122-22-22-2-200-1-1-11-11112i−2i00002i2i−2i−2i-220i3−i300i3i3−i3−i3−ii00−i−iii0000-100001−3−333000000
χ2122-2-2-111-122-22-22-2-200-1-1-11-1111−2i2i0000−2i−2i2i2i-220−i3i300−i3−i3i3i3i−i00ii−i−i0000-100001−3−333000000
χ2222-2-2-111-122-22-22-2-200-1-1-11-1111−2i2i0000−2i−2i2i2i-220i3−i300i3i3−i3−i3i−i00ii−i−i0000-10000133−3−3000000
χ232-22-222-2-2222-2-2-22-22i−2i22-22-22-2-2002i2i−2i−2i000000000000000002i−2i000000−i2i2000000−i2i2−i2i200002−2
χ242-22-222-2-2222-2-2-22-22i−2i22-22-22-2-2002i2i−2i−2i000000000000000002i−2i000000i2−i2000000i2−i2i2−i20000−22
χ252-22-222-2-2222-2-2-22-2−2i2i22-22-22-2-200−2i−2i2i2i00000000000000000−2i2i000000−i2i2000000−i2i2−i2i20000−22
χ262-22-222-2-2222-2-2-22-2−2i2i22-22-22-2-200−2i−2i2i2i00000000000000000−2i2i000000i2−i2000000i2−i2i2−i200002−2
χ27444444441-2-211-21-2441-211-2-2-21221111-1-1-1-10000000000022-2-2-1-1-1-122000-1-1-1-100000000000
χ28444444441-2-211-21-2441-211-2-2-21-2-21111111100000000000-2-2-2-21111-2-2000111100000000000
χ29444444441-2-211-21-2-4-41-211-2-2-2122-1-1-1-1-1-1-1-1000000000002222-1-1-1-1-2-2000111100000000000
χ30444444441-2-211-21-2-4-41-211-2-2-21-2-2-1-1-1-1111100000000000-2-222111122000-1-1-1-100000000000
χ3144444444-211-2-21-2144-21-2-2111-200-2-2-2-2000000222-1-1-1-1-1-100110000000000000000002-1-1000
χ3244444444-211-2-21-2144-21-2-2111-200-2-2-2-2000000-2-2-21111110011000000000000000000-211000
χ3344444444-211-2-21-21-4-4-21-2-2111-2002222000000222-1-1-1-1-1-100-1-1000000000000000000-211000
χ3444444444-211-2-21-21-4-4-21-2-2111-2002222000000-2-2-211111100-1-10000000000000000002-1-1000
χ354444-2-2-2-24444444400-2-2-2-2-2-2-2-20000000000-4-40000000000000000000002000020000000000
χ3644-4-44-4-441-221-1-2-12001-21-1-222-12i−2i3-33-3−i−iii000000000002i−2i00−i−iii2i−2i000−i−iii00000000000
χ3744-4-44-4-441-221-1-2-12001-21-1-222-12i−2i-33-33−i−iii000000000002i−2i00−i−iii−2i2i000ii−i−i00000000000
χ3844-4-44-4-441-221-1-2-12001-21-1-222-1−2i2i3-33-3ii−i−i00000000000−2i2i00ii−i−i−2i2i000ii−i−i00000000000
χ3944-4-44-4-441-221-1-2-12001-21-1-222-1−2i2i-33-33ii−i−i00000000000−2i2i00ii−i−i2i−2i000−i−iii00000000000
χ4044-4-4-222-244-44-44-4-400-2-2-22-222200000000004-400000000000000000000020000-20000000000
χ414-44-444-4-41-2-2-1-12124i−4i1-2-112-22-100ii−i−i3−33−30000000000000−2i2i3−33−300000−i3i3−i3i300000000000
χ424-44-444-4-41-2-2-1-12124i−4i1-2-112-22-100ii−i−i−33−330000000000000−2i2i−33−3300000i3−i3i3−i300000000000
χ434-44-444-4-41-2-2-1-1212−4i4i1-2-112-22-100−i−iii3−33−300000000000002i−2i3−33−300000i3−i3i3−i300000000000
χ444-44-444-4-41-2-2-1-1212−4i4i1-2-112-22-100−i−iii−33−3300000000000002i−2i−33−3300000−i3i3−i3i300000000000
χ454-44-444-4-4-21122-1-2-14i−4i-212-2-11-1200−2i−2i2i2i000000000−i3i3−i3i3−i3i300i−i00000000000000000003−3000
χ464-44-444-4-4-21122-1-2-14i−4i-212-2-11-1200−2i−2i2i2i000000000i3−i3i3−i3i3−i300i−i0000000000000000000−33000
χ474-44-444-4-4-21122-1-2-1−4i4i-212-2-11-12002i2i−2i−2i000000000−i3i3−i3i3−i3i300−ii0000000000000000000−33000
χ484-44-444-4-4-21122-1-2-1−4i4i-212-2-11-12002i2i−2i−2i000000000i3−i3i3−i3i3−i300−ii00000000000000000003−3000
χ494-44-4-2-222444-4-4-44-400-2-22-22-2220000000000000000000000000000000−2i22i2000000i2−i2i2−i2000000
χ504-44-4-2-222444-4-4-44-400-2-22-22-22200000000000000000000000000000002i2−2i2000000−i2i2−i2i2000000
χ514-4-444-44-41-22-112-1-2001-2-1-122-21003i−3i−3i3i−i3i3i3−i3000000000000000−i3i3i3−i300000−333−300000000000
χ524-4-444-44-41-22-112-1-2001-2-1-122-21003i−3i−3i3ii3−i3−i3i3000000000000000i3−i3−i3i3000003−3−3300000000000
χ534-4-444-44-41-22-112-1-2001-2-1-122-2100−3i3i3i−3i−i3i3i3−i3000000000000000−i3i3i3−i3000003−3−3300000000000
χ544-4-444-44-41-22-112-1-2001-2-1-122-2100−3i3i3i−3ii3−i3−i3i3000000000000000i3−i3−i3i300000−333−300000000000
χ554-4-444-44-444-4-44-4-440044-4-4-4-4440000000000000000000000000000000000000000000000000
χ564-4-44-22-2244-4-44-4-4400-2-22222-2-2000000000000000000000000000000000000000i6−i6−i6i6000000
χ574-4-44-22-2244-4-44-4-4400-2-22222-2-2000000000000000000000000000000000000000−i6i6i6−i6000000
χ588888-4-4-4-42-4-422-42-400-12-1-1222-1440000-2-2-2-200000000000-2-200111100000000000000000000
χ598888-4-4-4-42-4-422-42-400-12-1-1222-1-4-400002222000000000002200-1-1-1-100000000000000000000
χ608888-4-4-4-4-422-4-42-42002-122-1-1-120000000000004-2-2-2-211110000000000000000000000000000
χ618888-4-4-4-4-422-4-42-42002-122-1-1-12000000000000-42222-1-1-1-10000000000000000000000000000
χ6288-8-88-8-88-42-2-4424-200-42-442-2-240000000000000000000000000000000000000000000000000
χ6388-8-8-444-42-442-2-4-2400-12-112-2-214i−4i0000−2i−2i2i2i00000000000−2i2i00ii−i−i00000000000000000000
χ6488-8-8-444-42-442-2-4-2400-12-112-2-21−4i4i00002i2i−2i−2i000000000002i−2i00−i−iii00000000000000000000
χ6588-8-8-444-4-42-2-4424-2002-12-2-111-20000000000000−2i32i300i3i3−i3−i30000000000000000000000000000
χ6688-8-8-444-4-42-2-4424-2002-12-2-111-200000000000002i3−2i300−i3−i3i3i30000000000000000000000000000
χ678-88-8-4-4442-4-4-2-242400-121-1-22-2100000023−2323−23000000000000000−33−3300000000000000000000
χ688-88-8-4-4442-4-4-2-242400-121-1-22-21000000−2323−23230000000000000003−33−300000000000000000000
χ698-88-8-4-444-42244-2-4-2002-1-221-11-2000000000000000−2i32i3i3−i3i3−i30000000000000000000000000000
χ708-88-8-4-444-42244-2-4-2002-1-221-11-20000000000000002i3−2i3−i3i3−i3i30000000000000000000000000000
χ718-8-888-88-8-42-24-4-24200-4244-2-22-40000000000000000000000000000000000000000000000000
χ728-8-88-44-442-44-224-2-400-1211-2-22-1000000−2i32i32i3−2i3000000000000000i3−i3−i3i300000000000000000000
χ738-8-88-44-442-44-224-2-400-1211-2-22-10000002i3−2i3−2i32i3000000000000000−i3i3i3−i300000000000000000000
χ748-8-88-44-44-42-24-4-242002-1-2-211-12000000000000000003-3-330000000000000000000000000000
χ758-8-88-44-44-42-24-4-242002-1-2-211-1200000000000000000-333-30000000000000000000000000000

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