Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #13096 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C13 · Schur multiplier (H2) = C24 |
| direct product | C13×#13099 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C13 | #1898 |
| commutator | C22×C4 | C22×C4×C13 |
| Frattini, cosocle | C2×#41 | C23×C13 |
| prime radical | C13×#3008 | C2 |
| LCS | G ▷ C22×C4 ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C13 ◁ C2×C4×C13 ◁ C2×C13×H(5,𝔽2) ◁ G | |
666 conjugacy classes of subgroups.
| minimal degree | μ(G) = 45 |
| transitive degree | μt(G) = 416 |
A minimal faithful permutation representation — 3 generators on 45 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13)(14,15,19,24)(16,25)(17,31)(18,23,35,40)(20,27,38,28)(21,34)(22,26)(29,42)(30,43)(32,39)(33,36)(37,44,41,45);(14,16,26,28,19,30,17,27)(15,20,31,43,24,38,22,25)(18,33,34,44,35,29,32,45)(21,36,23,41,39,42,40,37);(14,17,19,26)(15,21,24,39)(16,27,30,28)(18,34,35,32)(20,36,38,42)(22,40,31,23)(25,37,43,41)(29,45,33,44)442 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 6087);