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×#33833 |
| 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 | |
692 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)(20,28)(21,27)(22,36)(24,25)(26,31)(29,41)(30,42)(32,45)(34,35)(37,39)(40,44)(43,49)(46,48);(18,20)(19,26)(21,29)(22,37)(23,28)(24,39)(25,30)(27,40)(31,36)(32,46)(33,41)(34,48)(35,43)(38,42)(44,45)(47,49);(15,17)(18,21,25,35)(19,27,24,34)(20,29,30,43)(22,32,36,45)(23,33,38,47)(26,40,39,48)(28,41,42,49)(31,44,37,46);(18,22)(19,23)(20,30)(21,32)(24,38)(25,36)(27,33)(28,37)(29,43)(31,42)(34,47)(35,45)(41,46)(44,49)559 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 26821);