Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #19368 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C17 · Schur multiplier (H2) = C24 |
| direct product | C17×#19383 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C17 | C2×#121 |
| commutator, Frattini, cosocle | C42 | C24×C17 |
| prime radical | C17×#3251 | C2 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C17 ◁ C2×C42×C17 ◁ G | |
606 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)(18,19,23,26)(20,27,29,32)(21,25,22,31)(24,30,33,28)(34,35)(36,44)(37,43)(38,40)(39,42)(41,45)(46,49)(47,48);(18,20,22,28,23,29,21,30)(19,24,25,27,26,33,31,32)(35,40)(41,48)(42,43)(44,49);(18,19)(20,24)(21,31)(22,25)(23,26)(27,28)(29,33)(30,32)(34,36)(35,41)(37,45)(38,46)(39,47)(40,48)(42,44)(43,49);(18,21,23,22)(19,25,26,31)(20,28,29,30)(24,32,33,27)(34,37,38,39)(35,42,40,43)(36,45,46,47)(41,44,48,49)629 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 12371);