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×#23414 |
| 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 | |
1980 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)(16,24)(17,21)(18,30)(19,23)(20,26)(22,32)(25,40)(27,38)(28,36)(29,44)(31,34)(33,45)(35,42)(37,43)(39,41);(14,16)(15,20)(17,25)(18,31)(19,27)(21,35)(22,38)(23,34)(24,30)(26,32)(28,41)(29,45)(33,36)(37,39)(40,44)(42,43);(14,17)(15,21)(16,25)(18,29)(19,28)(20,33)(22,37)(23,36)(24,39)(26,42)(27,41)(30,44)(31,45)(32,43)(34,35)(38,40);(17,28)(21,36)(25,41)(29,43)(33,35)(37,44)(39,40)(42,45)598 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 16402);