Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 2 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C13 · Schur multiplier (H2) = C27×C4 |
| direct product | C13×#36687 |
| subgroup | G/H | |
|---|---|---|
| center | C22×C4×C13 | C24 |
| commutator, Frattini, cosocle | C23 | C25×C13 |
| socle | C23×C13 | C25 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C22×C4×C13 ◁ G | |
2446 conjugacy classes of subgroups.
| minimal degree | μ(G) = 41 |
| transitive degree | μt(G) = 1664 |
A minimal faithful permutation representation — 5 generators on 41 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13)(14,15,16,17)(18,19)(20,22)(21,23)(24,25)(26,27)(28,32)(29,33)(30,31)(34,37)(35,39)(36,38)(40,41);(18,20,21,25)(19,22,23,24)(27,31)(32,37)(33,38)(39,41);(15,17)(18,19)(20,24)(21,23)(22,25)(26,28)(27,32)(29,35)(30,34)(31,37)(33,39)(36,40)(38,41);(19,23)(22,24)(28,34)(32,37)(35,40)(39,41);(26,29,30,36)(27,33,31,38)(28,35,34,40)(32,39,37,41)676 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 29675);