Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #24274 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C13 · Schur multiplier (H2) = C25 |
| direct product | C13×#25135 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C13 | C22×D4 |
| commutator, Frattini, cosocle | C22×C4 | C24×C13 |
| prime radical | C13×#2407 | C2 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C13 ◁ C2×C4×D4×C13 ◁ G | |
1124 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)(14,15)(16,17)(22,23,26,32,28,33,27,31)(24,29,34,37,35,30,25,36);(15,17)(18,19)(20,21)(22,24,26,34,28,35,27,25)(23,29,32,37,33,30,31,36);(19,21)(22,25,28,34)(23,30,33,29)(24,26,35,27)(31,36,32,37);(15,17)(22,26,28,27)(23,31,33,32)(24,25,35,34)(29,37,30,36)598 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 18123);