Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C17 · Schur multiplier (H2) = C25 |
| direct product | C17×#19007 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C17 | C2×#120 |
| commutator, Frattini, cosocle | C42 | C24×C17 |
| prime radical | C22×D4×C17 | D4 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C17 ◁ C2×C42×C17 ◁ G | |
862 conjugacy classes of subgroups.
| minimal degree | μ(G) = 49 |
| transitive degree | μt(G) = 1088 |
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)(18,19,22,24)(20,26,28,33)(21,29,31,25)(23,30,32,27)(34,35,39,36)(37,44,45,49)(38,43,48,41)(40,47,42,46);(18,20)(19,23)(21,30)(22,28)(24,32)(25,33)(26,29)(27,31)(34,36,39,35)(37,42,45,40)(38,41,48,43)(44,47,49,46);(21,31)(25,29)(26,33)(27,30)(34,37)(35,40)(36,42)(38,47)(39,45)(41,49)(43,44)(46,48);(19,24)(23,32)(25,29)(26,33)578 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 11995);