Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #11549 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C13 · Schur multiplier (H2) = C2×C4 |
| direct product | C13×#13303 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C13 | C2×#99 |
| commutator | C22×C4 | C22×C4×C13 |
| Frattini, cosocle | C22×Q8 | C23×C13 |
| prime radical | C23×C13 | C2×C22⋊C4 |
| LCS | G ▷ C22×C4 ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C13 ◁ C22×C4×C13 ◁ C2×C4×Q8×C13 ◁ G | |
396 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)(16,20)(17,18)(19,21)(22,23,27,31,28,32,25,29)(24,33,35,26,30,34,37,36);(15,18)(19,20)(22,24,34,31,28,30,33,29)(23,27,37,26,32,25,35,36);(14,16,17,21)(15,19,18,20)(22,25,28,27)(23,29,32,31)(24,35,30,37)(26,34,36,33)481 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 6291);