Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #11663 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C13 · Schur multiplier (H2) = C23 |
| direct product | C13×#11663 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C13 | C2×#102 |
| commutator | C2×C8 | C22×C4×C13 |
| Frattini, cosocle | C4×C8 | C23×C13 |
| prime radical | C22×C13×D8 | C4 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C13 ◁ C2×C42×C13 ◁ C2×C4×C8×C13 ◁ G | |
426 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)(14,15,16,19,17,18,20,21)(22,23,25,30,26,28,36,31)(24,32,34,29,35,27,33,37);(23,27)(24,33)(25,36)(28,32)(29,30)(31,37)(34,35);(15,18)(19,21)(23,28)(27,32)(29,37)(30,31)598 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 4651);