Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #33688 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C13 · Schur multiplier (H2) = C24 |
| direct product | C13×#33690 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C13 | #3109 |
| commutator, Frattini, cosocle | C2×C8 | C24×C13 |
| prime radical | C13×#2190 | C2 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C13 ◁ C2×C4×C13 ◁ C4×C13×M16 ◁ G | |
526 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)(16,21)(17,27)(18,31)(19,35)(20,24)(22,30)(23,32)(25,42)(26,41)(28,40)(29,44)(33,36)(34,39)(37,43)(38,45);(14,16,20,19)(15,21,24,35)(17,25,29,28)(18,32,34,26)(22,36,37,38)(23,39,41,31)(27,40,44,42)(30,45,43,33);(14,17)(15,22)(16,25)(18,33)(19,28)(20,29)(21,36)(23,40)(24,37)(26,43)(27,31)(30,32)(34,45)(35,38)(39,44)(41,42);(17,28,29,25)(18,34)(22,36,37,38)(23,41)(26,32)(27,40,44,42)(30,33,43,45)(31,39)442 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 26678);