Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #8412 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C13 · Schur multiplier (H2) = C24 |
| direct product | C13×#8424 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C13 | #379 |
| commutator | C42 | C22×C4×C13 |
| Frattini, cosocle | C2×C42 | C23×C13 |
| prime radical | C2×C13×#41 | D4 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C13 ◁ C2×C42×C13 ◁ G | |
734 conjugacy classes of subgroups.
| minimal degree | μ(G) = 37 |
| transitive degree | μt(G) = 832 |
A minimal faithful permutation representation — 3 generators on 37 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13)(14,15,18,21,19,16,17,20)(22,23)(24,31,33,27)(25,30)(26,29)(28,32,36,34)(35,37);(14,16,19,15)(17,20,18,21)(22,24)(23,27)(25,32)(26,33)(28,30)(29,31)(34,35)(36,37);(22,24)(23,28)(25,34)(26,33)(27,30)(29,36)(31,37)(32,35)559 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 1412);