Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #13442 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C13 · Schur multiplier (H2) = C23 |
| direct product | C13×#13442 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C13 | #2054 |
| commutator, Frattini, cosocle | C22×C8 | C23×C13 |
| prime radical | C2×C13×#509 | C2 |
| LCS | G ▷ C22×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C13 ◁ C22×C4×C13 ◁ C13×#405 ◁ G | |
398 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)(15,22)(16,28)(17,33)(18,19)(20,34)(24,37)(25,27)(26,35)(29,38)(30,44)(31,36)(32,42)(39,43)(41,45);(14,15)(16,29)(17,24)(18,25)(19,35)(20,37)(21,27)(22,33)(23,30)(26,34)(28,39)(31,45)(32,41)(36,40)(38,44)(42,43);(14,16,17,30,34,44,18,28,21,32,19,36,20,31,33,42)(15,23,22,29,37,43,35,45,27,40,25,41,26,39,24,38)442 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 6430);