Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #13307 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C13 · Schur multiplier (H2) = C24 |
| direct product | C13×#13338 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C13 | #447 |
| commutator, Frattini, cosocle | C22×C8 | C23×C13 |
| prime radical | C13×#3155 | C2 |
| LCS | G ▷ C22×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C13 ◁ C22×C4×C13 ◁ C13×#405 ◁ G | |
566 conjugacy classes of subgroups.
| minimal degree | μ(G) = 49 |
| transitive degree | μt(G) = 832 |
A minimal faithful permutation representation — 3 generators on 49 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13)(18,19,24,30)(20,31,34,43)(21,25,22,38)(23,41,37,29)(26,44,47,33)(27,39,28,35)(32,45,42,48)(36,46,40,49);(14,15)(16,17)(19,25)(20,32)(21,35)(22,39)(23,37)(26,45)(27,29)(28,41)(30,38)(31,49)(33,44)(34,42)(43,46)(47,48);(15,17)(18,20)(19,26)(21,36)(22,40)(23,42)(24,34)(25,43)(27,45)(28,48)(29,49)(30,47)(31,38)(32,37)(33,39)(35,44)(41,46)520 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 6326);