Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #18132 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C17 · Schur multiplier (H2) = C25 |
| direct product | C17×#18156 |
| 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 | |
982 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)(19,25)(21,34)(22,30)(26,42)(27,44)(28,41)(29,36)(31,48)(37,47)(39,40)(43,45)(46,49);(18,19)(20,26)(21,27)(22,36)(23,29)(24,28)(25,30)(31,45)(32,43)(33,40)(34,39)(35,44)(37,49)(38,46)(41,47)(42,48);(18,20,23,32)(19,26,29,43)(21,30,34,22)(24,33,38,35)(25,39,36,27)(28,40,46,44)(31,47,48,37)(41,42,49,45);(18,21,24,31)(19,27,28,45)(20,30,33,47)(22,35,37,32)(23,34,38,48)(25,40,41,26)(29,39,46,42)(36,44,49,43)629 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 11144);