Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #23400 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C13 · Schur multiplier (H2) = C26 |
| direct product | C13×#23494 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C13 | C2×#120 |
| commutator, Frattini, cosocle | C22×C4 | C24×C13 |
| prime radical | C22×C13×#41 | C22 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C13 ◁ C23×C4×C13 ◁ G | |
1362 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)(15,16)(18,19)(20,24)(21,31)(22,34)(23,27)(25,33)(26,37)(28,45)(29,43)(30,40)(32,44)(35,39)(36,42)(38,47)(41,48)(46,49);(14,15)(16,17)(18,20,23,30)(19,24,27,40)(21,28,32,46)(22,35,37,29)(25,41,42,38)(26,43,34,39)(31,45,44,49)(33,48,36,47);(14,16,17,15)(18,21)(19,25)(20,28)(22,36)(23,32)(24,38)(26,44)(27,42)(29,48)(30,46)(31,34)(33,37)(35,47)(39,49)(40,41)(43,45);(21,32)(25,42)(28,46)(31,44)(33,36)(38,41)(45,49)(47,48)598 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 16482);