Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #33605 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C13 · Schur multiplier (H2) = C24×C4 |
| direct product | C13×#33719 |
| 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 ◁ C2×C42×C13 ◁ C2×C4×C8×C13 ◁ G | |
834 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)(15,17)(18,19)(20,28)(21,33)(22,25)(23,36)(24,31)(26,29)(27,34)(30,40)(32,47)(35,48)(37,45)(38,49)(39,44)(41,43)(42,46);(18,20,29,43,23,32,35,45,22,30,44,49,34,46,21,31)(19,24,33,42,27,38,39,40,25,37,48,47,36,41,26,28);(14,15,16,17)(19,25)(24,37)(26,39)(27,36)(28,40)(33,48)(38,41)(42,47);(20,30)(24,37)(28,40)(31,45)(32,46)(38,41)(42,47)(43,49)676 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 26707);