Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #11704 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C13 · Schur multiplier (H2) = C2×C4 |
| direct product | C13×#11750 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C13 | C2×#102 |
| commutator | C2×C8 | C22×C4×C13 |
| Frattini, cosocle | C22×C8 | C23×C13 |
| prime radical | C13×#466 | C22 |
| LCS | G ▷ C2×C8 ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C13 ◁ C2×C42×C13 ◁ C2×C4×C8×C13 ◁ G | |
326 conjugacy classes of subgroups.
| minimal degree | μ(G) = 53 |
| transitive degree | μt(G) = 1664 |
A minimal faithful permutation representation — 3 generators on 53 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13)(15,19,20,21)(22,23,26,31,28,33,27,32)(24,34,37,47,35,50,38,51)(25,39,41,30,43,48,42,49)(29,40,45,36,44,53,46,52);(14,15)(16,19)(17,21)(18,20)(22,24)(23,29)(25,40)(26,38)(27,37)(28,35)(30,47)(31,46)(32,45)(33,44)(34,48)(36,42)(39,50)(41,52)(43,53)(49,51);(14,16,18,17)(15,19,20,21)(24,35)(29,44)(34,50)(36,52)(37,38)(40,53)(45,46)(47,51)598 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 4738);