Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 2 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4×C13 · Schur multiplier (H2) = C28 |
| direct product | C13×#34373 |
| 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 | |
1998 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)(20,24)(21,22)(23,25)(27,31)(28,34)(29,37)(39,41);(19,22)(23,24)(26,27,30,31)(28,35,34,32)(29,33,37,38)(36,41,40,39);(26,28,30,34)(27,32,31,35)(29,36,37,40)(33,39,38,41);(18,19)(20,23)(21,22)(24,25)(26,27)(28,32)(29,33)(30,31)(34,35)(36,39)(37,38)(40,41);(18,20,21,25)(19,23,22,24)(26,29,30,37)(27,33,31,38)(28,36,34,40)(32,39,35,41)988 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 27361);