Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #7694 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C13 · Schur multiplier (H2) = C2×C4 |
| direct product | C13×#7726 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C13 | C2×C22⋊C4 |
| commutator | C22×C4 | C22×C4×C13 |
| Frattini, cosocle | C2×C42 | C23×C13 |
| prime radical | C22×D4×C13 | C2×C4 |
| LCS | G ▷ C22×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C23×C13 ◁ C43×C13 ◁ G | |
400 conjugacy classes of subgroups.
| minimal degree | μ(G) = 53 |
| transitive degree | μt(G) = 1664 |
A minimal faithful permutation representation — 3 generators on 53 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13)(14,15,17,19,18,21,16,20)(22,23)(24,30,32,27)(25,33)(26,29)(28,34)(31,35,37,36)(38,39)(40,46,48,53)(41,45)(42,44)(43,47,51,49)(50,52);(15,19)(16,17)(20,21)(22,24)(23,27)(25,31)(26,32)(28,35)(29,30)(33,36)(34,37)(38,40)(39,43)(41,49)(42,48)(44,51)(45,53)(46,52)(47,50);(14,16,18,17)(15,19,21,20)(22,25,26,34)(23,28,29,33)(24,31,32,37)(27,35,30,36)(39,44)(43,51)(45,52)(46,53)598 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 714);