Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 4 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C13 · Schur multiplier (H2) = C26 |
| direct product | C13×#33530 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C13 | #447 |
| commutator, Frattini, cosocle | C2×C8 | C24×C13 |
| socle | C2×C13 | C2×#447 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C13 ◁ C22×C4×C13 ◁ C22×C13×M16 ◁ G | |
1132 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)(16,25)(17,22)(18,30)(19,34)(20,24)(21,27)(23,33)(26,42)(28,41)(29,40)(31,36)(32,44)(35,39)(37,43)(38,45);(14,16)(15,21)(17,26)(18,31)(19,35)(20,28)(22,36)(23,39)(24,37)(25,30)(27,33)(29,43)(32,45)(34,38)(40,42)(41,44);(18,32)(23,40)(25,41)(27,43)(29,33)(30,44)(31,45)(39,42);(14,17,20,19)(15,22,24,34)(16,26,28,35)(18,29,32,33)(21,36,37,38)(23,30,40,44)(25,42,41,39)(27,31,43,45)520 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 26518);