Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #23391 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C17 · Schur multiplier (H2) = C24 |
| direct product | C17×#23826 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C17 | C22×D4 |
| commutator, Frattini, cosocle | C22×C4 | C24×C17 |
| prime radical | C22×D4×C17 | C23 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C17 ◁ C43×C17 ◁ G | |
746 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)(18,19,22,24)(20,25,21,23)(26,27,29,31)(28,32,33,30)(34,35,39,43)(36,40,46,49)(37,41,38,42)(44,47,45,48);(18,20,22,21)(19,23,24,25)(26,28,29,33)(27,30,31,32)(34,36)(35,40)(37,45)(38,44)(39,46)(41,48)(42,47)(43,49);(27,31)(30,32)(36,44)(37,38)(40,47)(41,42)(45,46)(48,49);(18,21,22,20)(19,23,24,25)(34,37,39,38)(35,41,43,42)(36,45,46,44)(40,48,49,47)884 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 16814);