Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #23903 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C13 · Schur multiplier (H2) = C27 |
| direct product | C13×#23905 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C13 | C2×#120 |
| commutator, Frattini, cosocle | C24 | C24×C13 |
| prime radical | C13×#3485 | C2 |
| LCS | G ▷ C24 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C13 ◁ C23×C4×C13 ◁ G | |
1744 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)(20,24,30,37)(21,25,32,39)(22,33,34,26)(28,40,42,35)(29,43,44,36)(31,38,45,46)(41,48,49,47);(14,15)(16,17)(18,20,23,30)(19,24,27,37)(21,28,32,42)(22,29,34,44)(25,35,39,40)(26,36,33,43)(31,41,45,49)(38,47,46,48);(15,17)(18,21)(19,25)(20,28)(22,31)(23,32)(24,35)(26,38)(27,39)(29,41)(30,42)(33,46)(34,45)(36,47)(37,40)(43,48)(44,49);(18,22)(19,26)(20,29)(21,31)(23,34)(24,36)(25,38)(27,33)(28,41)(30,44)(32,45)(35,47)(37,43)(39,46)(40,48)(42,49)520 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 16893);