Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 2 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4×C13 · Schur multiplier (H2) = C28 |
| direct product | C13×#34378 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C13 | C25 |
| commutator | C22 | C24×C4×C13 |
| Frattini, cosocle | C23 | C25×C13 |
| prime radical | C24×C13 | C24 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C23×C13 ◁ G | |
2010 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)(19,22)(20,24)(26,27)(28,35)(29,32)(30,38)(31,34)(33,39)(36,40)(37,41);(19,22)(23,25)(26,28,31,29)(27,32,34,35)(30,36,39,37)(33,40,38,41);(18,19)(20,23)(21,22)(24,25)(26,29,31,28)(27,32,34,35)(30,37,39,36)(33,40,38,41);(18,20,21,24)(19,23,22,25)(26,27)(28,35)(29,32)(30,33)(31,34)(36,41)(37,40)(38,39);(26,30)(27,33)(28,36)(29,37)(31,39)(32,40)(34,38)(35,41)988 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 27366);