Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #18346 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C17 · Schur multiplier (H2) = C24×C4 |
| direct product | C17×#18370 |
| 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 | |
1024 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)(20,22)(21,33)(26,42)(27,40)(28,37)(29,41)(31,46)(32,38)(34,49)(35,48)(36,45)(39,44)(43,47);(18,19)(20,25)(21,34)(22,37)(23,28)(24,29)(26,36)(27,30)(31,47)(32,41)(33,43)(35,39)(38,40)(42,46)(44,45)(48,49);(18,20,30,38)(19,25,27,40)(21,31,45,46)(22,24,32,23)(26,39,43,49)(28,37,29,41)(33,48,36,35)(34,47,44,42);(18,21,30,45)(19,26,27,43)(20,31,38,46)(22,35,32,48)(23,36,24,33)(25,39,40,49)(28,34,29,44)(37,47,41,42)578 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 11358);