Finite Group Databasebeta

← Group #13048775

Character table — Group #13048775

Order 1296.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72
size112222222222222222266669912121212121212121212121212121212121212121212181818181818181818181818181818181854545454108108108108
order122333366666666666633664433333666666666666666664121212121212121212121212121212122244661212
χ1111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1
χ311111111111111111111111-1-11111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-11-11-11-1
χ411111111111111111111111-1-11111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-11-11-11
χ511-11111-1-1-1-1-1-1-1-1111111111111111-1-111111-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11-1-111-1-11
χ611-11111-1-1-1-1-1-1-1-1111111111111111-1-111111-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-111-1-111-1
χ711-11111-1-1-1-1-1-1-1-111111111-1-111111-1-111111-1-1-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-11111111111-1-111-1-1
χ811-11111-1-1-1-1-1-1-1-111111111-1-111111-1-111111-1-1-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-111111111-1-111-1-111
χ922222222222222222222-12-1002-1-1-1-12-12-1-1-1-122-1-1-1-1-1-1-1-10000000000000000002020-10-1
χ1022222222222222222222-12-1002-1-1-1-12-12-1-1-1-122-1-1-1-1-1-1-1-1000000000000000000-20-20101
χ112222222222222222222-12-1200-12-1-1-1-12-12-1-1-1-1-122-1-1-1-1-1-1000000000000000002020-10-10
χ122222222222222222222-12-1200-12-1-1-1-12-12-1-1-1-1-122-1-1-1-1-1-100000000000000000-20-201010
χ132222-1-1-122-1-1-1-1-1-12-1-1-1222222-1-12-1-122-1-12-1-1-1-1-1-122-1-1-1-1222-1-1-1-1-1-122-1-1-1-1-1-100000000
χ142222-1-1-122-1-1-1-1-1-12-1-1-12222-2-2-1-12-1-122-1-12-1-1-1-1-1-122-1-1-1-1-2-2-2111111-2-211111100000000
χ1522-22222-2-2-2-2-2-2-2-222222-12-1002-1-1-1-1-212-1-1-1-1-2-21111111100000000000000000020-20-101
χ1622-22222-2-2-2-2-2-2-2-222222-12-1002-1-1-1-1-212-1-1-1-1-2-211111111000000000000000000-202010-1
χ1722-22222-2-2-2-2-2-2-2-22222-12-1200-12-1-1-11-2-12-1-1-111-2-21111110000000000000000020-20-1010
χ1822-22222-2-2-2-2-2-2-2-22222-12-1200-12-1-1-11-2-12-1-1-111-2-211111100000000000000000-202010-10
χ1922-22-1-1-1-2-21111112-1-1-1222222-1-12-1-1-2-2-1-12-1-11111-2-21111-222-1-1-1-1-1-1-2-211111100000000
χ2022-22-1-1-1-2-21111112-1-1-12222-2-2-1-12-1-1-2-2-1-12-1-11111-2-211112-2-211111122-1-1-1-1-1-100000000
χ212-20222200000000-2-2-2-222-2-22i−2i2222200-2-2-2-2-2000000000002i−2i2i2i2i−2i−2i−2i0000000000000000
χ222-20222200000000-2-2-2-222-2-2−2i2i2222200-2-2-2-2-200000000000−2i2i−2i−2i−2i2i2i2i0000000000000000
χ232-202-1-1-100−i3−i3−i3i3i3i3-211122-2-22i−2i-1-12-1-10011-211−i3i3−i3i300−i3−i3i3i302i−2i−i−i−iiii00333−3−3−300000000
χ242-202-1-1-100−i3−i3−i3i3i3i3-211122-2-2−2i2i-1-12-1-10011-211−i3i3−i3i300−i3−i3i3i30−2i2iiii−i−i−i00−3−3−333300000000
χ252-202-1-1-100i3i3i3−i3−i3−i3-211122-2-22i−2i-1-12-1-10011-211i3−i3i3−i300i3i3−i3−i302i−2i−i−i−iiii00−3−3−333300000000
χ262-202-1-1-100i3i3i3−i3−i3−i3-211122-2-2−2i2i-1-12-1-10011-211i3−i3i3−i300i3i3−i3−i30−2i2iiii−i−i−i00333−3−3−300000000
χ274444444444444444444-2-2-2-200-2-2111-2-2-2-2111-2-2-2-21111110000000000000000000000000
χ284444-2-2-244-2-2-2-2-2-24-2-2-24-24-200-21-2114-2-21-211-2-211-2-211110000000000000000000000000
χ294444-2-2-244-2-2-2-2-2-24-2-2-2-24-24001-2-211-241-2-21111-2-2-2-211110000000000000000000000000
χ304444-2-2-244-2-2-2-2-2-24-2-2-2-2-2-2-200111−1−3i32−1+3i32-2-2111−1−3i32−1+3i32111111−1−3i32−1+3i32−1−3i32−1+3i320000000000000000000000000
χ314444-2-2-244-2-2-2-2-2-24-2-2-2-2-2-2-200111−1+3i32−1−3i32-2-2111−1+3i32−1−3i32111111−1+3i32−1−3i32−1+3i32−1−3i320000000000000000000000000
χ3244-44444-4-4-4-4-4-4-4-44444-2-2-2-200-2-211122-2-21112222-1-1-1-1-1-10000000000000000000000000
χ3344-44-2-2-2-4-42222224-2-2-24-24-200-21-211-42-21-21122-1-122-1-1-1-10000000000000000000000000
χ3444-44-2-2-2-4-42222224-2-2-2-24-24001-2-2112-41-2-211-1-12222-1-1-1-10000000000000000000000000
χ3544-44-2-2-2-4-42222224-2-2-2-2-2-2-200111−1−3i32−1+3i3222111−1−3i32−1+3i32-1-1-1-1-1-11+3i321−3i321+3i321−3i320000000000000000000000000
χ3644-44-2-2-2-4-42222224-2-2-2-2-2-2-200111−1+3i32−1−3i3222111−1+3i32−1−3i32-1-1-1-1-1-11−3i321+3i321−3i321+3i320000000000000000000000000
χ374-40444400000000-4-4-4-44-2-42004-2-2-2-200-4222200000000000000000000000000000000000
χ384-40444400000000-4-4-4-4-242-400-24-2-2-2002-422200000000000000000000000000000000000
χ394-40444400000000-4-4-4-4-2-22200-2-21110022-1-1-100003-33-3-330000000000000000000000000
χ404-40444400000000-4-4-4-4-2-22200-2-21110022-1-1-10000-33-333-30000000000000000000000000
χ414-404-2-2-200−2i3−2i3−2i32i32i32i3-42224-2-4200-21-211002-12-1-1−2i32i3i3−i300i3i3−i3−i30000000000000000000000000
χ424-404-2-2-200−2i3−2i3−2i32i32i32i3-4222-242-4001-2-21100-122-1-1i3−i3−2i32i300i3i3−i3−i30000000000000000000000000
χ434-404-2-2-200−2i3−2i3−2i32i32i32i3-4222-2-22200111−1−3i32−1+3i3200-1-1-11+3i321−3i32i3−i3i3−i33-3−3−i323−i323+i32−3+i320000000000000000000000000
χ444-404-2-2-200−2i3−2i3−2i32i32i32i3-4222-2-22200111−1+3i32−1−3i3200-1-1-11−3i321+3i32i3−i3i3−i3-333−i32−3−i32−3+i323+i320000000000000000000000000
χ454-404-2-2-2002i32i32i3−2i3−2i3−2i3-42224-2-4200-21-211002-12-1-12i3−2i3−i3i300−i3−i3i3i30000000000000000000000000
χ464-404-2-2-2002i32i32i3−2i3−2i3−2i3-4222-242-4001-2-21100-122-1-1−i3i32i3−2i300−i3−i3i3i30000000000000000000000000
χ474-404-2-2-2002i32i32i3−2i3−2i3−2i3-4222-2-22200111−1−3i32−1+3i3200-1-1-11+3i321−3i32−i3i3−i3i3-333+i32−3+i32−3−i323−i320000000000000000000000000
χ484-404-2-2-2002i32i32i3−2i3−2i3−2i3-4222-2-22200111−1+3i32−1−3i3200-1-1-11−3i321+3i32−i3i3−i3i33-3−3+i323+i323−i32−3−i320000000000000000000000000
χ49666-36-3-3-3-36-3-36-3-3-36-3-300002200000000000000000000002-1-12-1-12-1-1-1-12-1-12-1-100000000
χ50666-36-3-3-3-36-3-36-3-3-36-3-30000-2-20000000000000000000000-211-211-21111-211-21100000000
χ51666-3-36-3-3-3-36-3-36-3-3-36-300002200000000000000000000002-1-1-12-1-12-1-1-1-12-1-12-100000000
χ52666-3-36-3-3-3-36-3-36-3-3-36-30000-2-20000000000000000000000-2111-211-21111-211-2100000000
χ53666-3-3-36-3-3-3-36-3-36-3-3-3600002200000000000000000000002-1-1-1-12-1-12-1-1-1-12-1-1200000000
χ54666-3-3-36-3-3-3-36-3-36-3-3-360000-2-20000000000000000000000-21111-211-21111-211-200000000
χ5566-6-36-3-333-633-633-36-3-30000220000000000000000000000-2-1-12-1-12-1-111-211-21100000000
χ5666-6-36-3-333-633-633-36-3-30000-2-20000000000000000000000211-211-211-1-12-1-12-1-100000000
χ5766-6-3-36-3333-633-63-3-36-30000220000000000000000000000-2-1-1-12-1-12-1111-211-2100000000
χ5866-6-3-36-3333-633-63-3-36-30000-2-200000000000000000000002111-211-21-1-1-12-1-12-100000000
χ5966-6-3-3-363333-633-6-3-3-360000220000000000000000000000-2-1-1-1-12-1-121111-211-200000000
χ6066-6-3-3-363333-633-6-3-3-360000-2-2000000000000000000000021111-211-2-1-1-1-12-1-1200000000
χ616-60-36-3-3−3i33i30−3i33i303i3−3i33-63300002i−2i00000000000000000000000−ii2i−i−i−2iii3−303−30−3300000000
χ626-60-36-3-3−3i33i30−3i33i303i3−3i33-6330000−2i2i00000000000000000000000i−i−2iii2i−i−i−330−3303−300000000
χ636-60-36-3-33i3−3i303i3−3i30−3i33i33-63300002i−2i00000000000000000000000−ii2i−i−i−2iii−330−3303−300000000
χ646-60-36-3-33i3−3i303i3−3i30−3i33i33-6330000−2i2i00000000000000000000000i−i−2iii2i−i−i3−303−30−3300000000
χ656-60-3-36-3−3i33i33i30−3i3−3i303i333-6300002i−2i00000000000000000000000−ii−i2i−ii−2ii3−3−30330−300000000
χ666-60-3-36-3−3i33i33i30−3i3−3i303i333-630000−2i2i00000000000000000000000i−ii−2ii−i2i−i−3330−3−30300000000
χ676-60-3-36-33i3−3i3−3i303i33i30−3i333-6300002i−2i00000000000000000000000−ii−i2i−ii−2ii−3330−3−30300000000
χ686-60-3-36-33i3−3i3−3i303i33i30−3i333-630000−2i2i00000000000000000000000i−ii−2ii−i2i−i3−3−30330−300000000
χ696-60-3-3-36−3i33i3−3i33i303i3−3i30333-600002i−2i00000000000000000000000−ii−i−i2iii−2i3−33−30−33000000000
χ706-60-3-3-36−3i33i3−3i33i303i3−3i30333-60000−2i2i00000000000000000000000i−iii−2i−i−i2i−33−3303−3000000000
χ716-60-3-3-363i3−3i33i3−3i30−3i33i30333-600002i−2i00000000000000000000000−ii−i−i2iii−2i−33−3303−3000000000
χ726-60-3-3-363i3−3i33i3−3i30−3i33i30333-60000−2i2i00000000000000000000000i−iii−2i−i−i2i3−33−30−33000000000

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