Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #23860 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C13 · Schur multiplier (H2) = C25 |
| direct product | C13×#24748 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C13 | C22×D4 |
| commutator, Frattini, cosocle | C22×C4 | C24×C13 |
| prime radical | C22×D4×C13 | C23 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C13 ◁ C4×C13×C4⋊C4 ◁ G | |
976 conjugacy classes of subgroups.
| minimal degree | μ(G) = 37 |
| transitive degree | μt(G) = 1664 |
A minimal faithful permutation representation — 4 generators on 37 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13)(15,16)(18,19,20,21)(22,23)(24,28)(25,27)(26,29)(30,37)(31,34)(32,35)(33,36);(14,15,17,16)(23,27)(24,30)(26,32)(28,36)(31,33)(34,37);(19,21)(22,24,25,31)(23,28,27,34)(26,33,32,30)(29,36,35,37);(14,16,17,15)(23,27)(24,31)(29,35)(30,33)598 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 17736);