Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #33830 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C13 · Schur multiplier (H2) = C25 |
| direct product | C13×#33837 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C13 | C22×D8 |
| commutator, Frattini, cosocle | C2×C8 | C24×C13 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C13 ◁ C4×D4×C13 ◁ C8×D4×C13 ◁ G | |
680 conjugacy classes of subgroups.
| minimal degree | μ(G) = 49 |
| transitive degree | μt(G) = 1664 |
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)(19,25)(20,24)(21,29)(22,34)(26,42)(27,44)(28,41)(30,37)(31,46)(32,45)(33,39)(35,38)(40,47)(43,48);(18,19,23,28)(20,26,24,38)(21,31,33,44)(22,35,37,42)(25,30,41,34)(27,45,46,32)(29,48,39,40)(36,43,49,47);(15,17)(18,20,23,24)(19,26,28,38)(21,29,33,39)(22,30,37,34)(25,35,41,42)(27,43,46,47)(31,48,44,40)(32,36,45,49);(18,21,23,33)(19,27,28,46)(20,29,24,39)(22,36,37,49)(25,40,41,48)(26,43,38,47)(30,45,34,32)(31,42,44,35)559 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 26825);