Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #13307 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C13 · Schur multiplier (H2) = C23 |
| direct product | C13×#13384 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C13 | #447 |
| commutator, Frattini, cosocle | C22×C8 | C23×C13 |
| prime radical | C13×#3061 | C2 |
| LCS | G ▷ C22×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C13 ◁ C22×C4×C13 ◁ C2×C13×#131 ◁ G | |
408 conjugacy classes of subgroups.
| minimal degree | μ(G) = 49 |
| transitive degree | μt(G) = 1664 |
A minimal faithful permutation representation — 3 generators on 49 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13)(15,16)(18,19)(20,24)(21,25)(22,27)(23,29)(26,34)(28,35)(30,43)(31,40)(32,38)(33,39)(36,42)(37,44)(41,47)(45,49)(46,48);(14,15)(16,17)(18,20)(19,24)(21,31)(22,30)(23,33)(25,40)(26,37)(27,43)(28,38)(29,39)(32,35)(34,44)(36,45)(41,48)(42,49)(46,47);(14,16,17,15)(19,25)(20,30)(21,34)(22,35)(24,37)(26,28)(27,41)(29,42)(31,45)(32,33)(36,47)(38,49)(39,48)(40,43)520 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 6372);