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×#33839 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C13 | C22×D8 |
| commutator, Frattini, cosocle | C2×C8 | C24×C13 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C13 ◁ C4×D4×C13 ◁ C8×D4×C13 ◁ G | |
712 conjugacy classes of subgroups.
| minimal degree | μ(G) = 49 |
| transitive degree | μt(G) = 832 |
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)(18,19,23,28)(20,29,30,41)(21,34,37,43)(22,25,36,27)(24,39,40,32)(26,44,46,35)(31,47,48,42)(33,49,38,45);(18,20)(19,24)(21,31)(22,38)(23,30)(25,42)(26,45)(27,47)(28,40)(29,34)(32,35)(33,36)(37,48)(39,44)(41,43)(46,49);(15,17)(20,30)(24,40)(29,41)(31,48)(32,39)(33,38)(42,47)(45,49);(19,25)(20,31)(21,35)(22,36)(24,41)(27,28)(29,40)(30,48)(32,33)(34,43)(37,44)(38,39)(42,45)(47,49)559 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 26827);