Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C17 · Schur multiplier (H2) = C24 |
| direct product | C17×#19442 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C17 | C2×#121 |
| commutator, Frattini, cosocle | C42 | C24×C17 |
| prime radical | C17×#532 | C22 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C17 ◁ C2×C42×C17 ◁ G | |
578 conjugacy classes of subgroups.
| minimal degree | μ(G) = 49 |
| transitive degree | μt(G) = 2176 |
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)(18,19)(20,27)(21,25)(22,31)(23,26)(24,30)(28,33)(29,32)(34,35,40,43)(36,38,42,39)(37,44,47,45)(41,48,49,46);(18,20,22,30,23,28,21,29)(19,24,25,27,26,32,31,33)(34,36,38,43,40,42,39,35)(37,45,46,41,47,44,48,49);(20,28)(24,32)(27,33)(29,30)(34,37,40,47)(35,41,43,49)(36,44,42,45)(38,46,39,48);(18,21,23,22)(19,25,26,31)(20,29,28,30)(24,27,32,33)(34,38,40,39)(35,42,43,36)(37,46,47,48)(41,45,49,44)629 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 12430);