Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #18446 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C17 · Schur multiplier (H2) = C24×C4 |
| direct product | C17×#18459 |
| 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 ◁ C2×C42×C17 ◁ G | |
972 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)(21,32)(25,38)(26,36)(27,33)(29,31)(30,45)(34,47)(37,42)(39,49)(40,46)(41,48)(43,44);(18,19,22,27)(20,25,29,39)(21,33,32,24)(23,26,35,41)(28,42,31,40)(30,46,44,37)(34,48,47,36)(38,43,49,45);(20,29)(21,34)(24,36)(25,39)(28,31)(30,43)(32,47)(33,48)(37,38)(40,42)(44,45)(46,49);(18,20,23,31)(19,25,26,40)(21,30,34,45)(22,29,35,28)(24,37,36,49)(27,39,41,42)(32,44,47,43)(33,46,48,38)578 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 11447);