Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #24986 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C13 · Schur multiplier (H2) = C24 |
| direct product | C13×#24986 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C13 | #555 |
| commutator, Frattini, cosocle | C22×C4 | C24×C13 |
| socle | C2×C13 | #2420 |
| prime radical | C13×#3067 | C2 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C13 ◁ C22×C4×C13 ◁ G | |
642 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)(16,27)(17,31)(18,22)(19,36)(20,25)(21,26)(23,34)(24,30)(28,37)(29,38)(32,39)(33,41)(35,40)(42,43)(44,45);(14,16,19,18,21,30,20,29)(15,22,25,27,26,38,36,24)(17,32,34,28,35,43,33,44)(23,39,31,45,41,42,40,37);(14,17)(15,23)(16,28)(18,32)(19,33)(20,34)(21,35)(22,37)(24,39)(25,40)(26,41)(27,42)(29,43)(30,44)(31,36)(38,45);(14,18,19,30,21,29,20,16)(15,24,25,22,26,27,36,38)(17,32,33,44,35,43,34,28)(23,39,40,37,41,42,31,45)520 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 17974);