Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #33522 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C13 · Schur multiplier (H2) = C25 |
| direct product | C13×#33586 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C13 | C22×D8 |
| commutator, Frattini, cosocle | C2×C8 | C24×C13 |
| prime radical | C2×C13×#509 | C2 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C13 ◁ C13×#117 ◁ C13×#405 ◁ G | |
716 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)(18,19,23,28)(20,24,29,37)(21,25,34,41)(22,35,33,27)(26,42,40,32)(30,36,43,47)(31,46,44,39)(38,49,48,45);(14,15,16,17)(18,20)(19,24)(21,30)(22,31)(23,29)(25,36)(26,38)(27,39)(28,37)(32,45)(33,44)(34,43)(35,46)(40,48)(41,47)(42,49);(19,25)(21,32)(22,33)(24,36)(26,27)(28,41)(30,45)(31,44)(34,42)(35,40)(37,47)(38,39)(43,49)(46,48);(20,29)(24,37)(30,43)(31,44)(36,47)(38,48)(39,46)(45,49)598 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 26574);