Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 2 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C13 · Schur multiplier (H2) = C27 |
| direct product | C13×#34918 |
| subgroup | G/H | |
|---|---|---|
| center | C22×C4×C13 | C24 |
| commutator, Frattini, cosocle | C23 | C25×C13 |
| socle | C23×C13 | C25 |
| prime radical | C2×C13×#127 | C22 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C22×C4×C13 ◁ G | |
1992 conjugacy classes of subgroups.
| minimal degree | μ(G) = 37 |
| transitive degree | μt(G) = 1664 |
A minimal faithful permutation representation — 5 generators on 37 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13)(14,15,18,19)(16,20,17,21)(22,23,25,26)(24,28,29,27)(30,31,34,35)(32,37,33,36);(15,19)(20,21)(23,26)(27,28)(31,35)(32,33);(14,16,18,17)(15,20,19,21)(22,24,25,29)(23,27,26,28)(30,32,34,33)(31,36,35,37);(30,33,34,32)(31,36,35,37);(14,17,18,16)(15,21,19,20)988 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 27906);