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) = C25 |
| direct product | C13×#11324 |
| subgroup | G/H | |
|---|---|---|
| center, socle, prime radical | C24×C13 | C2×D4 |
| commutator | C22×C4 | C22×C4×C13 |
| Frattini, cosocle | C23×C4 | C23×C13 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C24×C13 ◁ C22×C42×C13 ◁ G | |
974 conjugacy classes of subgroups.
| minimal degree | μ(G) = 33 |
| transitive degree | μt(G) = 3328 |
A minimal faithful permutation representation — 3 generators on 33 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13)(15,17)(22,23,24,25)(27,30)(28,31)(32,33);(18,19)(20,21)(26,27,31,33,29,32,28,30);(14,15,16,17)(19,21)832 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 4312);