Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #24289 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C17 · Schur multiplier (H2) = C25 |
| direct product | C17×#25434 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C17 | D42 |
| commutator, Frattini, cosocle | C22×C4 | C24×C17 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C17 ◁ C22×C4×C17 ◁ G | |
1012 conjugacy classes of subgroups.
| minimal degree | μ(G) = 37 |
| transitive degree | μt(G) = 544 |
A minimal faithful permutation representation — 4 generators on 37 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17)(18,19,21,20)(22,23,26,29)(24,31,34,37)(25,30,32,28)(27,35,36,33);(18,20,21,19)(22,23,25,28,26,29,32,30)(24,27,33,31,34,36,35,37);(19,20)(22,23)(24,27)(25,28)(26,29)(30,32)(31,33)(34,36)(35,37);(22,24,32,35,26,34,25,33)(23,27,30,37,29,36,28,31)782 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 18422);