Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 2 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4×C13 · Schur multiplier (H2) = C28 |
| direct product | C13×#34244 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C13 | C25 |
| commutator | C22 | C24×C4×C13 |
| Frattini, cosocle | C23 | C25×C13 |
| prime radical | C2×C13×#121 | C22 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C23×C13 ◁ G | |
2186 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)(19,23)(24,25)(26,27)(28,32)(29,36)(30,31)(33,37)(34,40)(35,38)(39,41);(14,16,17,15)(27,31)(32,38)(33,36)(39,40);(18,19)(20,24)(21,25)(22,23)(26,28,30,35)(27,32,31,38)(29,34,37,41)(33,39,36,40);(18,20,22,21)(19,24,23,25)(26,27)(28,32)(29,33)(30,31)(34,39)(35,38)(36,37)(40,41);(18,21,22,20)(19,25,23,24)(26,29,30,37)(27,33,31,36)(28,34,35,41)(32,39,38,40)1144 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 27232);