Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #33469 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C13 · Schur multiplier (H2) = C25 |
| direct product | C13×#33469 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C13 | C2×#442 |
| commutator | C8 | C23×C4×C13 |
| Frattini, cosocle | C2×C8 | C24×C13 |
| prime radical | C13×#3414 | C2 |
| LCS | G ▷ C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C13 ◁ C22×C4×C13 ◁ C13×#405 ◁ G | |
646 conjugacy classes of subgroups.
| minimal degree | μ(G) = 45 |
| transitive degree | μt(G) = 416 |
A minimal faithful permutation representation — 4 generators on 45 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13)(15,20,22,35)(16,24)(17,27)(18,31)(21,37,38,45)(23,28,32,36)(25,42)(26,29)(30,33)(34,41,39,40);(14,15)(16,21)(17,28)(18,32)(19,22)(20,33)(23,31)(24,41)(25,38)(26,37)(27,35)(29,45)(30,36)(34,43)(39,44)(40,42);(14,16,18,24,19,25,31,42)(15,21,32,41,22,38,23,40)(17,29,27,44,30,26,33,43)(20,34,28,45,35,39,36,37);(16,25)(21,38)(24,42)(26,29)(34,39)(37,45)(40,41)(43,44)598 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 26457);