Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #23912 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C13 · Schur multiplier (H2) = C27 |
| direct product | C13×#23917 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C13 | C2×#120 |
| commutator, Frattini, cosocle | C22×C4 | C24×C13 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C13 ◁ C23×C4×C13 ◁ G | |
1682 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)(18,19)(20,25)(21,33)(22,27)(23,38)(24,29)(26,36)(28,31)(30,43)(32,42)(34,49)(35,45)(37,41)(39,44)(40,47)(46,48);(14,15)(16,17)(18,20,24,32)(19,25,29,42)(21,30,35,46)(22,23,37,31)(26,40,44,49)(27,38,41,28)(33,48,45,43)(34,39,47,36);(15,17)(18,21)(19,26)(20,30)(22,34)(23,39)(24,35)(25,40)(27,43)(28,45)(29,44)(31,36)(32,46)(33,38)(37,47)(41,48)(42,49);(18,22,24,37)(19,27,29,41)(20,31,32,23)(21,34,35,47)(25,28,42,38)(26,43,44,48)(30,36,46,39)(33,40,45,49)520 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 16905);