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×#18419 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C17 | C2×#120 |
| commutator, Frattini, cosocle | C22×C4 | C24×C17 |
| prime radical | C17×#3537 | C2 |
| LCS | G ▷ C22×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C17 ◁ C23×C4×C17 ◁ G | |
1062 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)(18,19,23,28)(20,30,33,46)(21,27,22,37)(24,29,40,45)(25,38,43,31)(26,39,35,36)(32,41,34,48)(42,47,44,49);(18,20)(19,25)(21,31)(22,38)(23,33)(24,34)(26,41)(27,46)(28,43)(29,44)(30,37)(32,40)(35,48)(36,47)(39,49)(42,45);(18,19)(20,25)(21,35)(22,26)(23,28)(24,29)(27,39)(30,47)(31,48)(32,42)(33,43)(34,44)(36,37)(38,41)(40,45)(46,49);(18,21,23,22)(19,26,28,35)(20,31,33,38)(24,36,40,39)(25,41,43,48)(27,45,37,29)(30,44,46,42)(32,49,34,47)629 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 11407);