Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 2 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C13 · Schur multiplier (H2) = C28 |
| direct product | C13×#36716 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C13 | C25 |
| commutator, Frattini, cosocle | C23 | C25×C13 |
| prime radical | C2×C13×#538 | C2 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C23×C13 ◁ G | |
2406 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)(23,25)(26,27)(28,35)(29,30)(31,39)(32,34)(33,40)(36,38)(37,41);(19,22)(23,25)(26,28,32,29)(27,30,34,35)(31,36,40,37)(33,38,39,41);(14,15)(16,17)(18,19)(20,23)(21,22)(24,25)(26,29,32,28)(27,30,34,35)(31,37,40,36)(33,38,39,41);(18,19)(20,23)(21,22)(24,25)(26,30)(27,28)(29,34)(31,38)(32,35)(33,36)(37,39)(40,41);(18,20)(19,23)(21,24)(22,25)(26,31)(27,33)(28,36)(29,37)(30,38)(32,40)(34,39)(35,41)676 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 29704);