Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #9303 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C13 · Schur multiplier (H2) = C23 |
| direct product | C13×#9304 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C13 | #386 |
| commutator | C42 | C22×C4×C13 |
| Frattini, cosocle | C2×C42 | C23×C13 |
| prime radical | C23×C13 | #121 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C13 ◁ C2×C42×C13 ◁ G | |
436 conjugacy classes of subgroups.
| minimal degree | μ(G) = 53 |
| transitive degree | μt(G) = 832 |
A minimal faithful permutation representation — 3 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)(24,28,33,43)(25,35)(26,38)(27,30)(29,36)(31,40)(32,46,47,53)(34,50,49,42)(37,45)(39,44)(41,51,52,48);(14,15,17,19,18,21,16,20)(22,24)(23,28,30,43)(25,32)(26,34)(27,33)(29,41,44,52)(31,42,38,50)(35,46,45,53)(36,48)(37,47)(39,51)(40,49);(14,16,18,17)(15,20,21,19)(22,25,27,37)(23,29,30,44)(24,32,33,47)(26,39,40,36)(28,41,43,52)(31,45,38,35)(34,51,49,48)(42,53,50,46)637 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 2292);