Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #13400 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C13 · Schur multiplier (H2) = C23 |
| direct product | C13×#13400 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C13 | #2034 |
| commutator, Frattini, cosocle | C22×C8 | C23×C13 |
| prime radical | C13×#3060 | C2 |
| LCS | G ▷ C22×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C13 ◁ C22×C4×C13 ◁ C2×C13×#131 ◁ G | |
402 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)(16,25)(17,31)(18,23)(19,37)(20,24)(21,28)(22,35)(26,33)(27,42)(29,43)(30,39)(32,34)(36,45)(38,44)(40,41);(14,15)(16,26)(17,32)(18,37)(19,23)(20,24)(21,29)(22,36)(25,41)(27,40)(28,39)(30,38)(31,34)(33,42)(35,45)(43,44);(14,16,19,29,20,27,18,30)(15,21,23,40,24,38,37,26)(17,33,35,44,36,41,34,28)(22,39,31,42,32,43,45,25)442 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 6388);