Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #18562 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C17 · Schur multiplier (H2) = C25 |
| direct product | C17×#18581 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C17 | C2×#120 |
| commutator, Frattini, cosocle | C42 | C24×C17 |
| prime radical | C17×#121 | D4 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C17 ◁ C2×C42×C17 ◁ G | |
866 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)(21,25,22,30)(24,31,33,28)(36,42)(37,44)(39,47)(40,45)(43,46)(48,49);(18,20)(19,24)(21,28)(22,31)(23,29)(25,32)(26,33)(27,30)(34,35,38,41)(36,39,43,48)(37,45,44,40)(42,49,46,47);(18,21,23,22)(19,25,26,30)(20,28,29,31)(24,32,33,27)(34,36)(35,39)(37,46)(38,43)(40,49)(41,48)(42,44)(45,47);(20,29)(24,33)(27,32)(28,31)680 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 11569);