Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 2 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C13 · Schur multiplier (H2) = C24×C4 |
| direct product | C13×#15343 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C24×C13 | C24 |
| commutator, Frattini, cosocle | C24 | C24×C13 |
| prime radical | C23×D4×C13 | C22 |
| LCS | G ▷ C24 ▷ C1 | |
| UCS | C1 ◁ C24×C13 ◁ G | |
1746 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)(15,17)(22,23,26,24)(25,28,29,27)(30,31,34,35)(32,36,37,33);(19,21)(23,24)(25,29)(30,32,34,37)(31,33,35,36);(18,19)(20,21)(22,24,26,23)(25,28,29,27)(30,32)(31,33)(34,37)(35,36);(14,15)(16,17)(22,25)(23,27)(24,28)(26,29)(30,33)(31,32)(34,36)(35,37)754 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 8331);