Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #33607 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C13 · Schur multiplier (H2) = C24×C4 |
| direct product | C13×#33722 |
| 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 ◁ C13×#117 ◁ C13×#405 ◁ G | |
826 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)(19,24)(21,32)(22,33)(25,34)(26,35)(27,39)(28,38)(30,45)(31,44)(36,37)(40,43)(41,46)(42,49)(47,48);(18,19,25,39,22,27,21,24,23,28,32,37,33,36,34,38)(20,26,40,49,31,42,30,35,29,41,45,48,44,47,43,46);(14,15,16,17)(18,20)(19,26)(21,30)(22,31)(23,29)(24,35)(25,40)(27,42)(28,41)(32,45)(33,44)(34,43)(36,47)(37,48)(38,46)(39,49);(20,29)(26,41)(30,43)(31,44)(35,46)(40,45)(42,47)(48,49)676 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 26710);