Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #33830 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C13 · Schur multiplier (H2) = C25 |
| direct product | C13×#33842 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C13 | C22×D8 |
| commutator, Frattini, cosocle | C2×C8 | C24×C13 |
| prime radical | C13×#3283 | C2 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C13 ◁ C4×D4×C13 ◁ C8×D4×C13 ◁ G | |
664 conjugacy classes of subgroups.
| minimal degree | μ(G) = 49 |
| transitive degree | μt(G) = 1664 |
A minimal faithful permutation representation — 4 generators on 49 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13)(14,15)(16,17)(18,19,24,21)(20,28,31,47)(22,35,39,46)(23,34,37,27)(25,42,32,30)(26,41,33,38)(29,48,40,44)(36,45,49,43);(18,20,24,31)(19,25,21,32)(22,36,39,49)(23,40,37,29)(26,44,33,48)(27,45,34,43)(28,46,47,35)(30,41,42,38);(15,17)(18,21,24,19)(20,25,31,32)(22,33,39,26)(23,34,37,27)(28,42,47,30)(29,43,40,45)(35,38,46,41)(36,44,49,48);(18,22)(19,26)(20,29)(21,33)(23,41)(24,39)(25,43)(27,46)(28,47)(30,42)(31,40)(32,45)(34,35)(37,38)559 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 26830);