Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42×C13 · Schur multiplier (H2) = C26 |
| direct product | C13×#10767 |
| 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 | |
1148 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)(14,15,18,25,20,24,19,23)(16,26,29,36,30,37,28,21)(17,31,33,39,34,22,32,38)(27,41,42,45,43,40,44,35);(14,16,19,28,20,30,18,29)(15,21,23,37,24,36,25,26)(17,27,33,42,34,43,32,44)(22,35,38,41,31,45,39,40);(14,17)(15,22)(16,27)(18,32)(19,33)(20,34)(21,35)(23,38)(24,31)(25,39)(26,40)(28,42)(29,44)(30,43)(36,45)(37,41)754 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 3755);