Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #7654 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C13 · Schur multiplier (H2) = C4 |
| direct product | C13×#7693 |
| subgroup | G/H | |
|---|---|---|
| center, socle, prime radical | C23×C13 | C2×C22⋊C4 |
| commutator | C22×C4 | C22×C4×C13 |
| Frattini, cosocle | C2×C42 | C23×C13 |
| LCS | G ▷ C22×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C23×C13 ◁ C43×C13 ◁ G | |
390 conjugacy classes of subgroups.
| minimal degree | μ(G) = 45 |
| transitive degree | μt(G) = 3328 |
A minimal faithful permutation representation — 3 generators on 45 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13)(15,19,20,21)(22,23,26,28,27,24,25,29)(30,31)(32,38,40,35)(33,41)(34,37)(36,42)(39,43,45,44);(14,15)(16,19)(17,21)(18,20)(22,24,27,23)(25,28,26,29)(30,32,34,40)(31,35,37,38)(33,39,42,45)(36,43,41,44);(14,16,18,17)(15,19,20,21)(22,25,27,26)(23,28,24,29)(30,33,34,42)(31,36,37,41)(32,39,40,45)(35,43,38,44)754 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 681);