Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #23996 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C13 · Schur multiplier (H2) = C26 |
| direct product | C13×#23997 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C13 | #2404 |
| commutator, Frattini, cosocle | C24 | C24×C13 |
| prime radical | C13×#3026 | C2 |
| LCS | G ▷ C24 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C13 ◁ C24×C13 ◁ G | |
1210 conjugacy classes of subgroups.
| minimal degree | μ(G) = 45 |
| transitive degree | μt(G) = 416 |
A minimal faithful permutation representation — 4 generators on 45 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13)(14,15)(16,20)(17,21)(18,22)(19,23)(24,31)(25,32)(26,33)(27,39)(28,41)(29,35)(30,36)(34,42)(37,45)(38,44)(40,43);(14,16,19,26)(15,20,23,33)(17,27)(18,25,30,38)(21,31)(22,32,36,44)(24,29)(28,40)(34,43)(35,39)(37,42)(41,45);(14,17)(15,21)(16,24)(18,28)(19,29)(20,31)(22,34)(23,35)(25,37)(26,27)(30,42)(32,43)(33,39)(36,41)(38,40)(44,45);(14,18)(15,22)(16,25)(17,28)(19,30)(20,32)(21,34)(23,36)(24,37)(26,38)(27,40)(29,42)(31,43)(33,44)(35,41)(39,45)520 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 16985);