Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 2 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C13 · Schur multiplier (H2) = C23×C4 |
| direct product | C13×#15500 |
| subgroup | G/H | |
|---|---|---|
| center, socle, prime radical | C24×C13 | C24 |
| commutator, Frattini, cosocle | C24 | C24×C13 |
| LCS | G ▷ C24 ▷ C1 | |
| UCS | C1 ◁ C24×C13 ◁ G | |
1326 conjugacy classes of subgroups.
| minimal degree | μ(G) = 37 |
| transitive degree | μt(G) = 3328 |
A minimal faithful permutation representation — 4 generators on 37 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13)(15,17)(19,21)(22,23,25,27)(24,26,28,29)(30,31)(32,36)(33,35)(34,37);(24,28)(26,29)(30,31,33,35)(32,36,37,34);(18,19,20,21)(22,24)(23,26)(25,28)(27,29)(30,31)(32,34)(33,35)(36,37);(14,15)(16,17)(22,23)(24,26)(25,27)(28,29)(30,32,33,37)(31,34,35,36)754 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 8488);