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×#13321 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C13 | #447 |
| commutator, Frattini, cosocle | C22×C8 | C23×C13 |
| prime radical | C13×#3058 | C2 |
| LCS | G ▷ C22×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C13 ◁ C22×C4×C13 ◁ C2×C13×#131 ◁ G | |
552 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)(20,31,34,46)(21,25,38,42)(22,29,23,28)(26,39,44,33)(27,37,41,35)(32,45,36,43)(40,48,47,49);(14,15)(16,17)(19,25)(21,35)(22,23)(26,40)(27,29)(28,41)(30,42)(31,45)(32,48)(33,39)(36,49)(37,38)(43,46)(44,47);(15,17)(18,20)(19,26)(21,36)(22,39)(23,33)(24,34)(25,40)(27,45)(28,46)(29,31)(30,44)(32,38)(35,49)(37,48)(41,43)(42,47)520 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 6309);