Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #24472 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C13 · Schur multiplier (H2) = C26 |
| direct product | C13×#24474 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C13 | #2410 |
| commutator, Frattini, cosocle | C22×C4 | C24×C13 |
| prime radical | C13×#3586 | C2 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C13 ◁ C22×C4×C13 ◁ G | |
1298 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)(14,15,19,24,20,18,37,23)(16,25,29,27,30,39,28,21)(17,31,35,33,36,41,34,22)(26,38,43,45,44,42,32,40);(14,16)(15,21)(17,32)(18,27)(19,29)(20,30)(22,40)(23,39)(24,25)(26,35)(28,37)(31,38)(33,45)(34,44)(36,43)(41,42);(14,17,20,36)(15,22,18,33)(16,26,30,44)(19,34,37,35)(21,38,27,42)(23,31,24,41)(25,40,39,45)(28,43,29,32);(14,18)(15,20)(16,27)(17,33)(19,23)(21,30)(22,36)(24,37)(25,28)(26,42)(29,39)(31,34)(32,45)(35,41)(38,44)(40,43)520 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 17462);