Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #18376 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C17 · Schur multiplier (H2) = C24×C4 |
| direct product | C17×#18400 |
| 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 | |
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)(19,26)(20,31)(21,33)(22,36)(27,42)(28,44)(29,37)(30,43)(32,35)(34,47)(38,39)(40,49)(41,45)(46,48);(18,19)(20,27)(21,34)(22,37)(23,40)(24,29)(25,30)(26,36)(28,31)(32,47)(33,45)(35,42)(38,43)(39,49)(41,46)(44,48);(18,20,25,21)(19,27,30,34)(22,35,39,32)(23,31,24,33)(26,41,43,44)(28,29,45,40)(36,46,38,48)(37,42,49,47);(18,21,25,20)(19,28,30,45)(22,35,39,32)(23,33,24,31)(26,42,43,47)(27,29,34,40)(36,46,38,48)(37,41,49,44)731 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 11388);