Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C17 · Schur multiplier (H2) = C25 |
| direct product | C17×#18121 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C17 | #120 |
| commutator, Frattini, cosocle | C22×C4 | C24×C17 |
| socle | C22×C17 | C2×#120 |
| prime radical | C17×#3460 | C2 |
| LCS | G ▷ C22×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C17 ◁ C23×C4×C17 ◁ G | |
990 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)(20,27)(21,25)(22,30)(23,26)(24,28)(29,32)(31,33)(34,35,38,41)(36,39,43,46)(37,40,44,47)(42,48,49,45);(18,20)(19,24)(21,28)(22,31)(23,29)(25,32)(26,33)(27,30)(34,36)(35,39)(37,42)(38,43)(40,45)(41,46)(44,49)(47,48);(34,37,38,44)(35,40,41,47)(36,42,43,49)(39,45,46,48);(18,21,23,22)(19,25,26,30)(20,28,29,31)(24,32,33,27)782 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 11109);