Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42×C13 · Schur multiplier (H2) = C26 |
| direct product | C13×#10766 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C13 | #379 |
| commutator | C2×C4 | C2×C42×C13 |
| Frattini, cosocle | C23×C4 | C23×C13 |
| socle | C2×C13 | C22⋊#95 |
| prime radical | C22×C13×#41 | C22 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C13 ◁ C23×C4×C13 ◁ G | |
1180 conjugacy classes of subgroups.
| minimal degree | μ(G) = 45 |
| transitive degree | μt(G) = 416 |
A minimal faithful permutation representation — 3 generators on 45 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13)(14,15)(16,25)(17,29,31,22)(18,33)(19,23)(20,24)(21,27)(26,40,42,39)(28,37)(30,38,32,44)(34,36)(35,41,43,45);(14,16,19,27,20,28,18,34)(15,21,23,37,24,36,33,25)(17,26,32,41,31,42,30,45)(22,35,38,40,29,43,44,39);(14,17)(15,22)(16,26)(18,30)(19,32)(20,31)(21,35)(23,38)(24,29)(25,39)(27,41)(28,42)(33,44)(34,45)(36,43)(37,40)754 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 3754);