Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #13313 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C13 · Schur multiplier (H2) = C23 |
| direct product | C13×#13440 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C13 | #466 |
| commutator, Frattini, cosocle | C22×C8 | C23×C13 |
| prime radical | C22×C13×D8 | C22 |
| LCS | G ▷ C22×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C13 ◁ C22×C4×C13 ◁ C13×#405 ◁ G | |
398 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)(14,15)(16,17)(18,19,24,30)(20,31,35,42)(21,25,22,38)(23,40,37,29)(26,32,44,33)(27,39,28,36)(34,41,47,45)(43,49,46,48);(19,25)(20,32)(21,36)(22,39)(23,37)(27,29)(28,40)(30,38)(31,45)(33,35)(34,49)(41,42)(43,46)(47,48);(15,17)(18,20,21,32,37,47,39,49,24,35,22,33,23,34,36,48)(19,26,27,42,40,46,38,45,30,44,28,31,29,43,25,41)520 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 6428);