Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 2 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C13 · Schur multiplier (H2) = C27 |
| direct product | C13×#36768 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C13 | C25 |
| commutator, Frattini, cosocle | C23 | C25×C13 |
| prime radical | C13×#2676 | C2 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C23×C13 ◁ G | |
1650 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)(14,15,17,18)(16,20,21,19)(24,28)(27,29)(32,36)(34,37);(15,18)(19,20)(23,26)(27,29)(30,31,33,35)(32,34,36,37);(22,23)(24,27)(25,26)(28,29)(30,32,33,36)(31,34,35,37);(14,15)(16,19)(17,18)(20,21)(22,23)(24,27)(25,26)(28,29);(14,16,17,21)(15,19,18,20)(22,24)(23,27)(25,28)(26,29)676 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 29756);