Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #18414 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C13 · Schur multiplier (H2) = C25 |
| direct product | C13×#18439 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C13 | C2×#120 |
| commutator, Frattini, cosocle | C22×C4 | C24×C13 |
| prime radical | C13×#3561 | C2 |
| LCS | G ▷ C22×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C13 ◁ C2×C42×C13 ◁ G | |
964 conjugacy classes of subgroups.
| minimal degree | μ(G) = 53 |
| transitive degree | μt(G) = 832 |
A minimal faithful permutation representation — 4 generators on 53 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13)(15,19)(16,17)(20,21)(22,23,27,31)(24,32,35,45)(25,29,36,43)(26,38,40,30)(28,39,42,34)(33,46,47,53)(37,50,49,44)(41,51,52,48);(14,15,18,20)(16,19,17,21)(22,24,27,35)(23,28,31,42)(25,33,36,47)(26,39,40,34)(29,41,43,52)(30,45,38,32)(37,51,49,48)(44,53,50,46);(16,17)(19,21)(22,25)(23,29)(24,33)(26,37)(27,36)(28,41)(30,44)(31,43)(32,46)(34,48)(35,47)(38,50)(39,51)(40,49)(42,52)(45,53);(14,16,18,17)(15,19,20,21)(25,36)(29,43)(33,47)(37,49)(41,52)(44,50)(46,53)(48,51)481 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 11427);