Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #18414 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C17 · Schur multiplier (H2) = C25 |
| direct product | C17×#18416 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C17 | C2×#120 |
| commutator, Frattini, cosocle | C22×C4 | C24×C17 |
| LCS | G ▷ C22×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C17 ◁ C23×C4×C17 ◁ G | |
978 conjugacy classes of subgroups.
| minimal degree | μ(G) = 49 |
| transitive degree | μt(G) = 544 |
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)(19,24)(20,28)(21,31)(25,37)(26,35)(27,32)(29,41)(30,44)(33,46)(36,39)(38,48)(40,47)(42,43)(45,49);(18,19,22,27)(20,25,29,38)(21,32,31,24)(23,26,34,40)(28,39,41,49)(30,45,43,36)(33,47,46,35)(37,42,48,44);(20,29)(21,33)(24,35)(25,38)(28,41)(30,44)(31,46)(32,47)(36,48)(37,45)(39,49)(42,43);(18,20)(19,25)(21,30)(22,29)(23,28)(24,36)(26,39)(27,38)(31,43)(32,45)(33,42)(34,41)(35,37)(40,49)(44,46)(47,48)629 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 11404);