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×#23916 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C13 | C2×#120 |
| commutator, Frattini, cosocle | C22×C4 | C24×C13 |
| prime radical | C13×#3487 | C2 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C13 ◁ C23×C4×C13 ◁ G | |
1694 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)(18,19,23,27)(20,28,30,42)(21,25,32,40)(22,34,35,26)(24,36,39,31)(29,45,46,44)(33,43,37,41)(38,48,49,47);(14,15)(16,17)(21,32)(22,35)(25,40)(26,34)(28,42)(29,46)(31,36)(38,49);(15,17)(18,20)(19,24)(21,29)(22,36)(23,30)(25,38)(26,42)(27,39)(28,34)(31,35)(32,46)(33,48)(37,47)(40,49)(41,44)(43,45);(18,21,23,32)(19,25,27,40)(20,29,30,46)(22,37,35,33)(24,38,39,49)(26,43,34,41)(28,44,42,45)(31,48,36,47)520 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 16904);