Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #23886 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C13 · Schur multiplier (H2) = C26 |
| direct product | C13×#24462 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C13 | D42 |
| commutator, Frattini, cosocle | C22×C4 | C24×C13 |
| prime radical | C2×C13×#578 | C2 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C13 ◁ C22×C4×C13 ◁ G | |
1302 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)(18,19,24,28)(20,30,33,40)(21,34,38,26)(22,32,25,41)(23,29,42,27)(31,47,49,44)(35,43,48,36)(37,45,39,46);(18,20,24,33)(19,25,28,22)(21,35,38,48)(23,41,42,32)(26,44,34,47)(27,40,29,30)(31,37,49,39)(36,45,43,46);(15,17)(18,21,24,38)(19,26,28,34)(20,31,33,49)(22,36,25,43)(23,37,42,39)(27,45,29,46)(30,44,40,47)(32,48,41,35);(18,22)(19,20)(21,36)(23,30)(24,25)(26,31)(27,41)(28,33)(29,32)(34,49)(35,45)(37,44)(38,43)(39,47)(40,42)(46,48)559 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 17450);