Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 2 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C13 · Schur multiplier (H2) = C25 |
| direct product | C13×#15139 |
| 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 | |
1250 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)(22,23,27,25)(24,29,26,28)(32,37)(33,35);(19,21)(22,24,27,26)(23,28,25,29)(30,31,34,36)(32,35,37,33);(18,19)(20,21)(22,25,27,23)(24,29,26,28)(30,32)(31,35)(33,36)(34,37);(14,15,16,17)(22,26,27,24)(23,29,25,28)(30,33,34,35)(31,32,36,37)832 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 8127);