Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #23387 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C13 · Schur multiplier (H2) = C25 |
| direct product | C13×#23814 |
| subgroup | G/H | |
|---|---|---|
| center, socle, prime radical | C23×C13 | C22×D4 |
| commutator, Frattini, cosocle | C22×C4 | C24×C13 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C13 ◁ C13×#376 ◁ G | |
926 conjugacy classes of subgroups.
| minimal degree | μ(G) = 57 |
| transitive degree | μt(G) = 3328 |
A minimal faithful permutation representation — 4 generators on 57 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13)(18,19,21,22)(20,23,24,25)(26,27,30,34,31,35,45,51)(28,36,39,47,38,49,43,32)(29,40,41,48,42,50,44,33)(37,46,54,57,53,56,55,52);(14,15)(16,17)(19,22)(23,25)(26,28,31,38)(27,32,35,47)(29,37,42,53)(30,43,45,39)(33,46,48,56)(34,49,51,36)(40,52,50,57)(41,55,44,54);(15,17)(26,29,31,42)(27,33,35,48)(28,37,38,53)(30,44,45,41)(32,46,47,56)(34,50,51,40)(36,52,49,57)(39,55,43,54);(18,20,21,24)(19,23,22,25)(28,38)(32,47)(36,49)(37,53)(39,43)(46,56)(52,57)(54,55)676 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 16802);