Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #25196 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C17 · Schur multiplier (H2) = C25 |
| direct product | C17×#25197 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C17 | #2424 |
| commutator, Frattini, cosocle | C22×C4 | C24×C17 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C17 ◁ C22×C4×C17 ◁ G | |
968 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)(18,19,23,27,24,28,22,36)(20,29,31,25,32,40,37,41)(21,33,34,43,35,42,38,26)(30,45,47,49,48,39,46,44);(18,20,23,31,24,32,22,37)(19,25,27,40,28,41,36,29)(21,30,34,47,35,48,38,46)(26,39,33,44,43,45,42,49);(18,21)(19,26)(20,30)(22,34)(23,38)(24,35)(25,39)(27,42)(28,43)(29,44)(31,46)(32,48)(33,36)(37,47)(40,49)(41,45);(18,19,24,28)(20,25,32,41)(21,26,35,43)(22,36,23,27)(29,31,40,37)(30,39,48,45)(33,38,42,34)(44,46,49,47)680 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 18185);