Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #9369 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C17 · Schur multiplier (H2) = C23 |
| direct product | C17×#9380 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C17 | #386 |
| commutator | C42 | C22×C4×C17 |
| Frattini, cosocle | C2×C42 | C23×C17 |
| prime radical | C23×C17 | #120 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C17 ◁ C2×C42×C17 ◁ G | |
424 conjugacy classes of subgroups.
| minimal degree | μ(G) = 49 |
| transitive degree | μt(G) = 1088 |
A minimal faithful permutation representation — 3 generators on 49 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17)(18,19)(20,28,21,24)(22,27)(23,26)(25,30,32,29)(31,33)(34,35,38,42,39,43,37,41)(36,44,46,40,47,48,45,49);(18,20,22,21)(19,24)(23,30,31,29)(25,26)(27,28)(32,33)(34,36)(35,40)(37,46)(38,45)(39,47)(41,48)(42,44)(43,49);(18,21,22,20)(19,25,27,32)(23,29,31,30)(24,26,28,33)(34,36)(35,40)(37,45)(38,46)(39,47)(41,44)(42,48)(43,49)629 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 2368);