Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #9996 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C13 · Schur multiplier (H2) = C23 |
| direct product | C13×#10000 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C13 | #392 |
| commutator, Frattini, cosocle | C2×C42 | C23×C13 |
| prime radical | C13×#2535 | C2 |
| LCS | G ▷ C2×C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C13 ◁ C2×C42×C13 ◁ G | |
632 conjugacy classes of subgroups.
| minimal degree | μ(G) = 37 |
| transitive degree | μt(G) = 416 |
A minimal faithful permutation representation — 3 generators on 37 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13)(14,15,17,20)(16,18,21,19)(22,23,27,31)(24,32,34,37)(25,30,26,29)(28,35,36,33);(15,18)(16,21)(19,20)(22,24)(23,28)(25,35)(26,33)(27,34)(29,37)(30,32)(31,36);(23,29)(25,26)(28,32)(30,31)(33,35)(36,37)481 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 2988);