Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #17547 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C13 · Schur multiplier (H2) = C25 |
| direct product | C13×#17653 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C13 | C22×C22⋊C4 |
| commutator | C2×C4 | C23×C4×C13 |
| Frattini, cosocle | C42 | C24×C13 |
| prime radical | C13×#3515 | C2 |
| LCS | G ▷ C2×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C13 ◁ C4×C13×#41 ◁ G | |
964 conjugacy classes of subgroups.
| minimal degree | μ(G) = 37 |
| transitive degree | μt(G) = 1664 |
A minimal faithful permutation representation — 4 generators on 37 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13)(15,18,19,20)(22,23,27,30,28,24,26,32)(25,29,35,36,33,31,34,37);(14,15)(16,20)(17,19)(18,21)(22,24,28,23)(25,31,33,29)(26,30,27,32)(34,36,35,37);(22,25)(23,29)(24,31)(26,34)(27,35)(28,33)(30,36)(32,37);(25,33)(29,31)(34,35)(36,37)793 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 10641);