Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 2 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4×C13 · Schur multiplier (H2) = C28 |
| direct product | C13×#34510 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C13 | C25 |
| commutator | C22 | C24×C4×C13 |
| Frattini, cosocle | C23 | C25×C13 |
| prime radical | C2×C13×#127 | C22 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C23×C13 ◁ G | |
2148 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)(14,15,17,16)(18,19)(20,24)(21,25)(22,23)(26,27,32,30)(28,35,29,33)(31,38,39,34)(36,40,37,41);(19,23)(20,25)(26,28,32,29)(27,33,30,35)(31,36,39,37)(34,40,38,41);(18,20)(19,21)(22,25)(23,24)(26,29,32,28)(27,33,30,35)(31,37,39,36)(34,40,38,41);(14,16,17,15)(18,20)(19,21)(22,25)(23,24)(26,30,32,27)(28,33,29,35)(31,38,39,34)(36,40,37,41);(18,21)(19,20)(22,24)(23,25)(26,31,32,39)(27,34,30,38)(28,36,29,37)(33,40,35,41)988 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 27498);