Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #9519 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C13 · Schur multiplier (H2) = C23 |
| direct product | C13×#9529 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C13 | #386 |
| commutator | C22×C4 | C22×C4×C13 |
| Frattini, cosocle | C2×C42 | C23×C13 |
| prime radical | C13×#3109 | C2 |
| LCS | G ▷ C22×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C13 ◁ C2×C42×C13 ◁ G | |
468 conjugacy classes of subgroups.
| minimal degree | μ(G) = 45 |
| transitive degree | μt(G) = 832 |
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)(16,23)(17,20)(22,27)(24,25)(26,28)(30,31,33,37,35,39,34,38)(32,40,41,36,42,44,43,45);(14,15,20,27,18,22,17,19)(16,21,23,28,25,29,24,26)(30,32)(31,36,39,45)(33,41)(34,43)(35,42)(37,44,38,40);(14,16)(15,21)(17,24)(18,25)(19,26)(20,23)(22,29)(27,28)(31,37)(33,34)(36,44)(38,39)(40,45)(41,43)481 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 2517);