Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #13417 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C13 · Schur multiplier (H2) = C23 |
| direct product | C13×#13417 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C13 | #2041 |
| commutator, Frattini, cosocle | C22×C8 | C23×C13 |
| prime radical | C13×#3155 | C2 |
| LCS | G ▷ C22×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C13 ◁ C22×C4×C13 ◁ C13×#405 ◁ G | |
454 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)(16,28)(17,22)(18,34)(19,25)(20,24)(21,27)(23,31)(26,36)(29,39)(30,42)(32,40)(33,44)(35,41)(37,43)(38,45);(15,22)(16,29)(17,20)(18,19)(23,40)(24,27)(25,44)(28,43)(30,31)(32,35)(33,36)(37,38)(39,42)(41,45);(14,16,17,30,21,32,20,38)(15,23,24,41,27,43,22,39)(18,35,33,31,36,29,19,37)(25,42,26,28,44,45,34,40)442 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 6405);