Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #10792 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42×C13 · Schur multiplier (H2) = C23×C4 |
| direct product | C13×#10810 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C13 | C4×C22⋊C4 |
| commutator | C2×C4 | C2×C42×C13 |
| Frattini, cosocle | C23×C4 | C23×C13 |
| socle | C2×C13 | #1434 |
| prime radical | C24×C13 | #41 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C13 ◁ C2×C13×#117 ◁ G | |
628 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)(16,25,29,40)(17,30)(18,23)(19,33)(20,24)(21,27,36,28)(22,31)(26,35,42,45)(32,37)(34,38)(39,43,44,41);(14,16)(15,21,24,36)(17,26)(18,27)(19,28)(20,29)(22,35,38,45)(23,25,33,40)(30,44,37,39)(31,41)(32,42)(34,43);(14,17,18,31,20,32,19,34)(15,22,23,37,24,38,33,30)(16,26,27,41,29,42,28,43)(21,35,25,39,36,45,40,44)754 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 3798);