Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #13309 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C13 · Schur multiplier (H2) = C23 |
| direct product | C13×#13395 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C13 | #469 |
| commutator, Frattini, cosocle | C22×C8 | C23×C13 |
| socle | C2×C13 | #2034 |
| prime radical | C13×#3050 | C2 |
| LCS | G ▷ C22×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C13 ◁ C22×C4×C13 ◁ C23×C8×C13 ◁ G | |
422 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)(16,24)(17,28)(18,33)(19,22)(20,26)(21,31)(23,30)(25,40)(27,37)(29,36)(32,44)(34,41)(35,42)(38,45)(39,43);(20,35)(24,40)(36,39)(37,41);(14,16,18,34,19,25,30,27)(15,20,23,39,22,35,33,36)(17,29,31,42,32,43,45,26)(21,37,28,40,38,41,44,24)520 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 6383);