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×#34177 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C13 | C25 |
| commutator | C22 | C24×C4×C13 |
| Frattini, cosocle | C23 | C25×C13 |
| prime radical | C25×C13 | C23 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C23×C13 ◁ G | |
2446 conjugacy classes of subgroups.
| minimal degree | μ(G) = 41 |
| transitive degree | μt(G) = 832 |
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)(20,24)(22,25)(26,27)(28,32)(29,36)(30,31)(33,37)(34,40)(35,38)(39,41);(18,19,21,23)(20,22,24,25)(27,31)(32,38)(33,36)(39,40);(18,20)(19,22)(21,24)(23,25)(26,28,30,35)(27,32,31,38)(29,34,37,41)(33,39,36,40);(26,27)(28,32)(29,33)(30,31)(34,39)(35,38)(36,37)(40,41);(26,29)(27,33)(28,34)(30,37)(31,36)(32,39)(35,41)(38,40)1144 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 27165);