Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #23414 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C13 · Schur multiplier (H2) = C27 |
| direct product | C13×#23434 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C13 | C2×#127 |
| commutator, Frattini, cosocle | C22×C4 | C24×C13 |
| socle | C2×C13 | C2×#392 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C13 ◁ C23×C4×C13 ◁ G | |
1916 conjugacy classes of subgroups.
| minimal degree | μ(G) = 45 |
| transitive degree | μt(G) = 416 |
A minimal faithful permutation representation — 4 generators on 45 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13)(14,15)(16,25)(17,30)(18,35)(19,24)(20,23)(21,27)(22,33)(26,43)(28,37)(29,38)(31,42)(32,40)(34,41)(36,44)(39,45);(14,16)(15,21)(17,31)(18,28)(19,27)(20,29)(22,39)(23,37)(24,38)(25,35)(26,32)(30,36)(33,44)(34,45)(40,42)(41,43);(14,17)(15,22)(16,26)(18,32)(19,33)(20,34)(21,36)(23,40)(24,41)(25,42)(27,31)(28,45)(29,44)(30,35)(37,43)(38,39);(15,23)(21,37)(22,40)(24,35)(25,38)(30,41)(36,43)(39,42)598 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 16422);