Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #23472 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C13 · Schur multiplier (H2) = C26 |
| direct product | C13×#23472 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C13 | C2×#124 |
| commutator, Frattini, cosocle | C22×C4 | C24×C13 |
| socle | C2×C13 | C2×#393 |
| prime radical | C22×C13×#41 | C22 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C13 ◁ C23×C4×C13 ◁ G | |
1148 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)(16,21)(17,29,31,40)(18,23)(19,34)(20,24)(22,32,39,33)(25,38,41,45)(26,36)(27,37)(28,43)(30,35,42,44);(14,16)(15,21)(17,30,31,42)(18,27)(19,28)(20,26)(22,38,39,45)(23,37)(24,36)(25,33,41,32)(29,44,40,35)(34,43);(14,17)(15,22)(16,25)(18,33)(19,32)(20,31)(21,35)(23,40)(24,39)(26,41)(27,30)(28,42)(29,34)(36,44)(37,45)(38,43);(16,26)(21,36)(25,41)(27,28)(30,42)(35,44)(37,43)(38,45)598 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 16460);