Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 2 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4×C13 · Schur multiplier (H2) = C27×C4 |
| direct product | C13×#34365 |
| 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 | |
2238 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)(27,31)(29,37)(32,34)(35,41);(19,22)(23,25)(26,27,30,31)(28,34,36,32)(29,33,37,38)(35,40,41,39);(18,19,21,22)(20,23,24,25);(18,20)(19,23)(21,24)(22,25)(26,28,30,36)(27,32,31,34)(29,35,37,41)(33,39,38,40);(26,29)(27,33)(28,35)(30,37)(31,38)(32,39)(34,40)(36,41)988 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 27353);