Finite Group Databasebeta

← Group #72221273

Character table — Group #72221273

Order 3200.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74
size1122244448888888888888881616161616161616161616161616161620202020252540405050508080808080808080100100100100100100100100100100100100200200200
order1224455101055810101010202020202020202010102020404040404040404040404040444422882442020202040404040444444444444448
χ111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11
χ3111111111111111111111111111111111111111111-1-1-1-11-1-1-1-111-1-111-1-1ii−i−iii−i−iii−i−ii−i-1
χ4111111111111111111111111111111111111111111-1-1-1-11-1-1-1-111-1-111-1-1−i−iii−i−iii−i−iii−ii-1
χ51111111111111111111111111111111111111111-1-111-1-1-11-1-1-1-1-111-1-111i−ii−ii−ii−iii−i−i−ii-1
χ61111111111111111111111111111111111111111-1-111-1-1-11-1-1-1-1-111-1-111−ii−ii−ii−ii−i−iiii−i-1
χ71111111111111111111111111111111111111111-1-1-1-111-1-1111-1-1-1-1-1-1-1-11-1-111-1-111111-1-11
χ81111111111111111111111111111111111111111-1-1-1-111-1-1111-1-1-1-1-1-1-1-1-111-1-111-1-1-1-1-1111
χ911111111111-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-11111111-1-1-1-111111111-1-1-1-1-1-1-1
χ1011111111111-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-11111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1
χ1111111111111-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-11-1-1-111-1-1-1-111ii−i−iii−i−i−i−iii−ii1
χ1211111111111-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-11-1-1-111-1-1-1-111−i−iii−i−iiiii−i−ii−i1
χ1311111111111-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11-1-1-1-1-1-11111-1-1i−ii−ii−ii−i−i−iiii−i1
χ1411111111111-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11-1-1-1-1-1-11111-1-1−ii−ii−ii−iiii−i−i−ii1
χ1511111111111-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111-1-1-1-111111-1-111-1-11-1-1-1-111-1
χ1611111111111-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111-1-1-1-11111-111-1-111-11111-1-1-1
χ17222-2-222222202222-2-2-2-2-2-2-2-222-2-20000000000002-22-222002-2-22-22-20000000000000000000
χ18222-2-222222202222-2-2-2-2-2-2-2-222-2-20000000000002-2-22-2-200-2222-2-220000000000000000000
χ19222-2-222222202222-2-2-2-2-2-2-2-222-2-2000000000000-222-2-2-200-222-222-20000000000000000000
χ20222-2-222222202222-2-2-2-2-2-2-2-222-2-2000000000000-22-2222002-2-2-22-220000000000000000000
χ2122-22-22222220-2-222-2-2-2-2-2-222-2-22200000000000000002200-22-2000000002002-200-20000000
χ2222-22-22222220-2-222-2-2-2-2-2-222-2-22200000000000000002200-22-200000000-200-220020000000
χ2322-22-22222220-2-222-2-2-2-2-2-222-2-2220000000000000000-2-2002-22000000002i00−2i−2i002i0000000
χ2422-22-22222220-2-222-2-2-2-2-2-222-2-2220000000000000000-2-2002-2200000000−2i002i2i00−2i0000000
χ2522-2-222222220-2-222222222-2-2-2-2-2-200000000000000002200-2-220000000002200-2-200000000
χ2622-2-222222220-2-222222222-2-2-2-2-2-200000000000000002200-2-22000000000-2-2002200000000
χ2722-2-222222220-2-222222222-2-2-2-2-2-20000000000000000-2-20022-20000000002i−2i00−2i2i00000000
χ2822-2-222222220-2-222222222-2-2-2-2-2-20000000000000000-2-20022-2000000000−2i2i002i−2i00000000
χ29444444-14-1-1-144-1-1-14-1-1-1-1-14-1-1-1-1-144-1-1-1-1-1-1-1-1-1-10044000400000-1-100-1-1000000000000000
χ30444444-14-1-1-144-1-1-14-1-1-1-1-14-1-1-1-1-144-1-1-1-1-1-1-1-1-1-100-4-4000-400000110011000000000000000
χ31444444-14-1-1-1-44-1-1-14-1-1-1-1-14-1-1-1-1-1-4-411111111110044000-400000-1-10011000000000000000
χ32444444-14-1-1-1-44-1-1-14-1-1-1-1-14-1-1-1-1-1-4-4111111111100-4-40004000001100-1-1000000000000000
χ3344444-14-14-1-14-14-1-1-14-1-1-1-1-14-1-1-1-1-1-144-1-1-1-1-1-1-1-144000040000-1-100-1-100000000000000000
χ3444444-14-14-1-14-14-1-1-14-1-1-1-1-14-1-1-1-1-1-144-1-1-1-1-1-1-1-1-4-40000-4000011001100000000000000000
χ3544444-14-14-1-1-4-14-1-1-14-1-1-1-1-14-1-1-1-111-4-411111111440000-40000-1-1001100000000000000000
χ3644444-14-14-1-1-4-14-1-1-14-1-1-1-1-14-1-1-1-111-4-411111111-4-40000400001100-1-100000000000000000
χ37444-4-44-14-1-1-104-1-1-1-411111-41-1-11100i5−i5i5i5i5i5−i5−i5−i5−i5004-4000000000-1100i5−i5000000000000000
χ38444-4-44-14-1-1-104-1-1-1-411111-41-1-11100i5−i5i5i5i5i5−i5−i5−i5−i500-440000000001-100−i5i5000000000000000
χ39444-4-44-14-1-1-104-1-1-1-411111-41-1-11100−i5i5−i5−i5−i5−i5i5i5i5i5004-4000000000-1100−i5i5000000000000000
χ40444-4-44-14-1-1-104-1-1-1-411111-41-1-11100−i5i5−i5−i5−i5−i5i5i5i5i500-440000000001-100i5−i5000000000000000
χ41444-4-4-14-14-1-10-14-1-11-411111-4-1-111i5−i500i5i5−i5−i5i5i5−i5−i54-4000000000-1100i5−i500000000000000000
χ42444-4-4-14-14-1-10-14-1-11-411111-4-1-111i5−i500i5i5−i5−i5i5i5−i5−i5-440000000001-100−i5i500000000000000000
χ43444-4-4-14-14-1-10-14-1-11-411111-4-1-111−i5i500−i5−i5i5i5−i5−i5i5i54-4000000000-1100−i5i500000000000000000
χ44444-4-4-14-14-1-10-14-1-11-411111-4-1-111−i5i500−i5−i5i5i5−i5−i5i5i5-440000000001-100i5−i500000000000000000
χ454-400044-4-444000-4-400000000000000000000000000004-40000000000000000000002-22-2000
χ464-400044-4-444000-4-400000000000000000000000000004-4000000000000000000000-22-22000
χ474-400044-4-444000-4-40000000000000000000000000000-440000000000000000000002i−2i−2i2i000
χ484-400044-4-444000-4-40000000000000000000000000000-44000000000000000000000−2i2i2i−2i000
χ4988888-2-2-2-23-28-2-23-2-2-233-2-2-2-23-23-2-2-2-2-233-2-2-2-2330000000000000000000000000000000000
χ5088888-2-2-2-23-2-8-2-23-2-2-233-2-2-2-23-23-22222-3-32222-3-30000000000000000000000000000000000
χ5188888-2-2-2-2-238-2-2-23-2-2-2-233-2-2-23-23-2-2-2-2-2-23333-2-20000000000000000000000000000000000
χ5288888-2-2-2-2-23-8-2-2-23-2-2-2-233-2-2-23-23222222-3-3-3-3220000000000000000000000000000000000
χ53888-8-8-2-2-2-23-20-2-23-222-3-322223-2-322i5−2i52i5−2i5−i5−i50000i5i50000000000000000000000000000000000
χ54888-8-8-2-2-2-23-20-2-23-222-3-322223-2-32−2i52i5−2i52i5i5i50000−i5−i50000000000000000000000000000000000
χ55888-8-8-2-2-2-2-230-2-2-232222-3-322-232-32i5−2i5−2i52i500i5i5−i5−i5000000000000000000000000000000000000
χ56888-8-8-2-2-2-2-230-2-2-232222-3-322-232-3−2i52i52i5−2i500−i5−i5i5i5000000000000000000000000000000000000
χ5788-88-88-28-2-2-20-82-2-2-8222228-222-2-20000000000000000000000000000000000000000000000
χ5888-88-8-28-28-2-202-8-2-22-82222-2822-2-20000000000000000000000000000000000000000000000
χ5988-88-8-2-2-2-23-20223-222-3-322-2-2-323-200005i−5i00005i−5i0000000000000000000000000000000000
χ6088-88-8-2-2-2-23-20223-222-3-322-2-2-323-20000−5i5i0000−5i5i0000000000000000000000000000000000
χ6188-88-8-2-2-2-2-23022-232222-3-3-2-22-3-230000005i−5i5i−5i000000000000000000000000000000000000
χ6288-88-8-2-2-2-2-23022-232222-3-3-2-22-3-23000000−5i5i−5i5i000000000000000000000000000000000000
χ6388-8-888-28-2-2-20-82-2-28-2-2-2-2-2-8222220000000000000000000000000000000000000000000000
χ6488-8-88-28-28-2-202-8-2-2-28-2-2-2-22-822220000000000000000000000000000000000000000000000
χ6588-8-88-2-2-2-23-20223-2-2-233-2-222-32-3200005−525−25−2525−550000000000000000000000000000000000
χ6688-8-88-2-2-2-23-20223-2-2-233-2-222-32-320000−55−252525−255−50000000000000000000000000000000000
χ6788-8-88-2-2-2-2-23022-23-2-2-2-233222-32-3000025−25−555−5−25250000000000000000000000000000000000
χ6888-8-88-2-2-2-2-23022-23-2-2-2-233222-32-30000−25255−5−5525−250000000000000000000000000000000000
χ6916-1600016-4-164-4-4000440000000000000000000000000000000000000000000000000000000000
χ7016-16000-4164-16-4-4000440000000000000000000000000000000000000000000000000000000000
χ7116-16000-4-4446-4000-640010i−10i000000000000000000000000000000000000000000000000000000
χ7216-16000-4-4446-4000-6400−10i10i000000000000000000000000000000000000000000000000000000
χ7316-16000-4-444-460004-6000010i−10i0000000000000000000000000000000000000000000000000000
χ7416-16000-4-444-460004-60000−10i10i0000000000000000000000000000000000000000000000000000

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