Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 2 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C13 · Schur multiplier (H2) = C27 |
| direct product | C13×#60042 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C13 | C25 |
| commutator, Frattini, cosocle | C23 | C25×C13 |
| prime radical | C22×D4×C13 | C23 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C23×C13 ◁ G | |
1648 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)(16,18)(17,20)(19,21)(30,31,35,34)(32,37,36,33);(15,16)(19,20)(24,28)(27,29)(32,36)(33,37);(14,15,18,16)(17,19,21,20)(22,23,26,25)(24,27,28,29)(30,32)(31,33)(34,37)(35,36);(14,16,18,15)(17,20,21,19)(22,24)(23,27)(25,29)(26,28)(30,33,35,37)(31,36,34,32);(14,17,18,21)(15,19,16,20)(22,25,26,23)(24,29,28,27)(30,34,35,31)(32,37,36,33)832 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 53030);