Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #1999 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C13 · Schur multiplier (H2) = C22 |
| direct product | C13×#8812 |
| subgroup | G/H | |
|---|---|---|
| center | C22×C4×C13 | C2×D4 |
| commutator | C22×C4 | C22×C4×C13 |
| Frattini, cosocle | C2×C42 | C23×C13 |
| socle, prime radical | C23×C13 | C2×C4⋊C4 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C4×C13 ◁ C43×C13 ◁ G | |
382 conjugacy classes of subgroups.
| minimal degree | μ(G) = 41 |
| transitive degree | μt(G) = 3328 |
A minimal faithful permutation representation — 3 generators on 41 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13)(15,17)(19,22)(20,24)(23,25)(26,27,29,32,30,33,36,39)(28,31,35,38,34,37,40,41);(18,19,20,22,21,23,24,25)(26,28)(27,31)(29,35)(30,34)(32,38)(33,37)(36,40)(39,41);(14,15,16,17)(19,23)(22,25)(28,34)(31,37)(35,40)(38,41)832 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 1800);