Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C13 · Schur multiplier (H2) = C28 |
| direct product | C13×#61499 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C13 | C23×D4 |
| commutator, Frattini, cosocle | C2×C4 | C25×C13 |
| prime radical | C13×#3522 | C2 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C13 ◁ C13×#529 ◁ G | |
1806 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)(15,18)(19,21)(22,23,28,32)(24,29,25,34)(26,31,27,36)(30,33,37,35);(14,15)(16,19)(17,18)(20,21)(22,24)(23,29)(25,28)(26,35)(27,33)(30,31)(32,34)(36,37);(22,25,28,24)(23,30,32,37)(26,35,27,33)(29,36,34,31);(15,18)(19,21);(14,16,17,20)(15,19,18,21)(22,26,28,27)(23,31,32,36)(24,33,25,35)(29,37,34,30)754 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 54487);