Finite Group Databasebeta

← Group #10591091

Character table — Group #10591091

Order 576.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69
size1111222222222222222244444444444444444444444444412121212121212121212121224242424242436363636
order12222233446666666666346666666661212121212121212121212121212121244441212121212121212246612128888
χ1111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1
χ411111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ51111-1-111111-1-1-1-1111111-1-1-111-1-1-1-111111-1-1-1-11111-1-1-1-111-1-11111-1-1-1-11-111-1-111-1-1
χ61111-1-111111-1-1-1-1111111-1-1-111-1-1-1-111111-1-1-1-11111-1-1-1-111-1-11111-1-1-1-1-11-1-111-1-111
χ71111-1-111111-1-1-1-1111111-1-1-111-1-1-1-111111-1-1-1-11111-1-1-1-1-1-111-1-1-1-111111-111-1-1-1-111
χ81111-1-111111-1-1-1-1111111-1-1-111-1-1-1-111111-1-1-1-11111-1-1-1-1-1-111-1-1-1-11111-11-1-11111-1-1
χ922222222-2-222222222222-2222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-20000000000000000000000
χ102222222-12222222-12-1-12-12-1-1-1-1-1-1-1-1-122-1-122-1-1-1-1-1-1-1-1-1-100000000000022-1-1-1-10000
χ112222222-12222222-12-1-12-12-1-1-1-1-1-1-1-1-122-1-122-1-1-1-1-1-1-1-1-1-1000000000000-2-211110000
χ122222222-1-2-222222-12-1-12-1-2-1-1-1-1-1-1-1-1-1-2-211-2-2111111111100000000000000−i3i3−i3i30000
χ132222222-1-2-222222-12-1-12-1-2-1-1-1-1-1-1-1-1-1-2-211-2-2111111111100000000000000i3−i3i3−i30000
χ14222222-1222-1-1-1-1-12-122-1-1222-1-1-1-1-1-1-1-1-122-1-122-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-10000000000
χ15222222-1222-1-1-1-1-12-122-1-1222-1-1-1-1-1-1-1-1-122-1-122-1-1-1-1-1-1-1-1-2-2-2-2111111110000000000
χ16222222-12-2-2-1-1-1-1-12-122-1-1-222-1-1-1-1-1-1-111-2-211-2-2111111110000−i3−i3i3i3−i3−i3i3i30000000000
χ17222222-12-2-2-1-1-1-1-12-122-1-1-222-1-1-1-1-1-1-111-2-211-2-2111111110000i3i3−i3−i3i3i3−i3−i30000000000
χ182222-2-222-2-22-2-2-2-22222222-2-222-2-2-2-22-2-2-2-22222-2-2-2-222220000000000000000000000
χ192222-2-22-1222-2-2-2-2-12-1-12-1-211-1-11111-122-1-1-2-211-1-1-1-111110000000000002-2-1-1110000
χ202222-2-22-1222-2-2-2-2-12-1-12-1-211-1-11111-122-1-1-2-211-1-1-1-11111000000000000-2211-1-10000
χ212222-2-22-1-2-22-2-2-2-2-12-1-12-1211-1-11111-1-2-21122-1-11111-1-1-1-100000000000000−i3i3i3−i30000
χ222222-2-22-1-2-22-2-2-2-2-12-1-12-1211-1-11111-1-2-21122-1-11111-1-1-1-100000000000000i3−i3−i3i30000
χ232222-2-2-1222-111112-122-1-1-2-2-2-1-11111-1-1-12211-2-2-1-1-1-1111122-2-2-1-1-1-111110000000000
χ242222-2-2-1222-111112-122-1-1-2-2-2-1-11111-1-1-12211-2-2-1-1-1-11111-2-2221111-1-1-1-10000000000
χ252222-2-2-12-2-2-111112-122-1-12-2-2-1-11111-111-2-2-1-1221111-1-1-1-10000−i3−i3i3i3i3i3−i3−i30000000000
χ262222-2-2-12-2-2-111112-122-1-12-2-2-1-11111-111-2-2-1-1221111-1-1-1-10000i3i3−i3−i3−i3−i3i3i30000000000
χ2722-2-200222-2-20000-222-2-22000-2-2000022-22-2000022-2-20000002i−2i00002i−2i2i−2i0000000000
χ2822-2-200222-2-20000-222-2-22000-2-2000022-22-2000022-2-2000000−2i2i0000−2i2i−2i2i0000000000
χ2922-2-20022-22-20000-222-2-22000-2-200002-22-220000-2-22200002i−2i002i−2i2i−2i00000000000000
χ3022-2-20022-22-20000-222-2-22000-2-200002-22-220000-2-2220000−2i2i00−2i2i−2i2i00000000000000
χ3122-2-200-122-21−i3−i3i3i3-2-12-21-100011−i3−i3i3i3-1-112-2−i3i300-1-111−i3−i3i3i3002i−2i3−3−33−ii−ii0000000000
χ3222-2-200-122-21−i3−i3i3i3-2-12-21-100011−i3−i3i3i3-1-112-2−i3i300-1-111−i3−i3i3i300−2i2i−333−3i−ii−i0000000000
χ3322-2-200-122-21i3i3−i3−i3-2-12-21-100011i3i3−i3−i3-1-112-2i3−i300-1-111i3i3−i3−i3002i−2i−333−3−ii−ii0000000000
χ3422-2-200-122-21i3i3−i3−i3-2-12-21-100011i3i3−i3−i3-1-112-2i3−i300-1-111i3i3−i3−i300−2i2i3−3−33i−ii−i0000000000
χ3522-2-200-12-221−i3−i3i3i3-2-12-21-100011−i3−i3i3i3-11-1-22i3−i30011-1-1i3i3−i3−i32i−2i00−ii−ii3−3−330000000000
χ3622-2-200-12-221−i3−i3i3i3-2-12-21-100011−i3−i3i3i3-11-1-22i3−i30011-1-1i3i3−i3−i3−2i2i00i−ii−i−333−30000000000
χ3722-2-200-12-221i3i3−i3−i3-2-12-21-100011i3i3−i3−i3-11-1-22−i3i30011-1-1−i3−i3i3i32i−2i00−ii−ii−333−30000000000
χ3822-2-200-12-221i3i3−i3−i3-2-12-21-100011i3i3−i3−i3-11-1-22−i3i30011-1-1−i3−i3i3i3−2i2i00i−ii−i3−3−330000000000
χ392-22-22-2220022-22-2-2-2-22-2202-22-22-22-2-20000000000000000000000000000000000−i2i2−i2i2
χ402-22-22-2220022-22-2-2-2-22-2202-22-22-22-2-20000000000000000000000000000000000i2−i2i2−i2
χ412-22-2-2222002-22-22-2-2-22-220-222-2-22-22-20000000000000000000000000000000000−i2i2i2−i2
χ422-22-2-2222002-22-22-2-2-22-220-222-2-22-22-20000000000000000000000000000000000i2−i2−i2i2
χ43444444-2-244-2-2-2-2-2-2-2-2-2-214-2-21111111-2-2-2-2-2-2-2-2111111110000000000000000000000
χ44444444-2-2-4-4-2-2-2-2-2-2-2-2-2-21-4-2-2111111122222222-1-1-1-1-1-1-1-10000000000000000000000
χ454444-4-4-2-244-22222-2-2-2-2-21-42211-1-1-1-11-2-2-2-222221111-1-1-1-10000000000000000000000
χ464444-4-4-2-2-4-4-22222-2-2-2-2-2142211-1-1-1-112222-2-2-2-2-1-1-1-111110000000000000000000000
χ4744-4-4004-24-4-4000024-22-4-2000220000-24-4-220000-2-22200000000000000000000000000
χ4844-4-4004-2-44-4000024-22-4-2000220000-2-442-2000022-2-200000000000000000000000000
χ4944-4-400-2-24-42−2i3−2i32i32i32-2-2221000-1-1i3i3−i3−i31-22-22−2i32i30011-1-1i3i3−i3−i30000000000000000000000
χ5044-4-400-2-24-422i32i3−2i3−2i32-2-2221000-1-1−i3−i3i3i31-22-222i3−2i30011-1-1−i3−i3i3i30000000000000000000000
χ5144-4-400-2-2-442−2i3−2i32i32i32-2-2221000-1-1i3i3−i3−i312-22-22i3−2i300-1-111−i3−i3i3i30000000000000000000000
χ5244-4-400-2-2-4422i32i3−2i3−2i32-2-2221000-1-1−i3−i3i3i312-22-2−2i32i300-1-111i3i3−i3−i30000000000000000000000
χ534-44-44-44-20044-44-42-42-2-4-20-22-22-22-22200000000000000000000000000000000000000
χ544-44-44-4-2400-2-22-22-42-442-204-4-22-22-22200000000000000000000000000000000000000
χ554-44-44-4-2-200-2-22-22222-2210-221-11-11-1-1000000003i−3i3i−3i3i−3i3i−3i0000000000000000000000
χ564-44-44-4-2-200-2-22-22222-2210-221-11-11-1-100000000−3i3i−3i3i−3i3i−3i3i0000000000000000000000
χ574-44-4-444-2004-44-442-42-2-4-202-2-222-22-2200000000000000000000000000000000000000
χ584-44-4-44-2400-22-22-2-42-442-20-44-222-22-2200000000000000000000000000000000000000
χ594-44-4-44-2-200-22-22-2222-22102-21-1-11-11-1000000003i−3i3i−3i−3i3i−3i3i0000000000000000000000
χ604-44-4-44-2-200-22-22-2222-22102-21-1-11-11-100000000−3i3i−3i3i3i−3i3i−3i0000000000000000000000
χ614-4-44004400-400004-4-4-444000-440000-400000000000000000000000000000000000000
χ624-4-44004-200-40000-2-4224-20002-20000200000023−23000023−23−23230000000000000000000000
χ634-4-44004-200-40000-2-4224-20002-200002000000−23230000−232323−230000000000000000000000
χ644-4-4400-24002−2i32i32i3−2i342-4-4-2-20002-2−2i32i32i3−2i3200000000000000000000000000000000000000
χ654-4-4400-240022i3−2i3−2i32i342-4-4-2-20002-22i3−2i3−2i32i3200000000000000000000000000000000000000
χ664-4-4400-2-2002−2i32i32i3−2i3-2222-21000-11i3−i3−i3i3-100000023−23−3i3i3i−3i−333−30000000000000000000000
χ674-4-4400-2-2002−2i32i32i3−2i3-2222-21000-11i3−i3−i3i3-1000000−23233i−3i−3i3i3−3−330000000000000000000000
χ684-4-4400-2-20022i3−2i3−2i32i3-2222-21000-11−i3i3i3−i3-100000023−233i−3i−3i3i−333−30000000000000000000000
χ694-4-4400-2-20022i3−2i3−2i32i3-2222-21000-11−i3i3i3−i3-1000000−2323−3i3i3i−3i3−3−330000000000000000000000

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