Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #24292 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C13 · Schur multiplier (H2) = C25 |
| direct product | C13×#24800 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C13 | D42 |
| commutator, Frattini, cosocle | C22×C4 | C24×C13 |
| prime radical | C2×C13×#135 | C22 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C13 ◁ C22×C4×C13 ◁ G | |
842 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)(18,19,23,29)(20,25,33,42)(21,34,37,45)(22,28,38,27)(24,32,40,31)(26,43,46,36)(30,47,35,39)(41,49,44,48);(18,20,22,31,23,33,38,32)(19,24,27,25,29,40,28,42)(21,30,36,48,37,35,43,49)(26,39,34,41,46,47,45,44);(15,17)(18,20)(19,25)(21,35)(22,31)(23,33)(24,28)(26,44)(27,40)(29,42)(30,37)(32,38)(34,39)(36,49)(41,46)(43,48)(45,47);(18,21,22,36,23,37,38,43)(19,26,27,34,29,46,28,45)(20,30,31,48,33,35,32,49)(24,39,25,41,40,47,42,44)520 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 17788);