Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C13 · Schur multiplier (H2) = C25 |
| direct product | C13×#22898 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C13 | D42 |
| commutator | C2×C4 | C23×C4×C13 |
| Frattini, cosocle | C22×C4 | C24×C13 |
| socle | C2×C13 | #2358 |
| prime radical | C13×#3018 | C2 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C13 ◁ C22×C4×C13 ◁ G | |
996 conjugacy classes of subgroups.
| minimal degree | μ(G) = 45 |
| transitive degree | μt(G) = 416 |
A minimal faithful permutation representation — 4 generators on 45 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13)(14,15,18,24,19,25,34,23)(16,22,28,37,29,36,27,20)(17,30,31,40,33,39,32,21)(26,41,43,45,44,35,42,38);(14,16,18,28,19,29,34,27)(15,20,24,22,25,37,23,36)(17,26,31,43,33,44,32,42)(21,35,30,38,40,41,39,45);(14,17)(15,21)(16,26)(18,31)(19,33)(20,35)(22,38)(23,39)(24,30)(25,40)(27,42)(28,43)(29,44)(32,34)(36,45)(37,41);(14,16)(15,22)(17,26)(18,28)(19,29)(20,23)(21,38)(24,37)(25,36)(27,34)(30,41)(31,43)(32,42)(33,44)(35,39)(40,45)676 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 15886);