Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #18224 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C17 · Schur multiplier (H2) = C25 |
| direct product | C17×#18236 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C17 | C2×#120 |
| commutator, Frattini, cosocle | C22×C4 | C24×C17 |
| prime radical | C17×#3537 | C2 |
| LCS | G ▷ C22×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C17 ◁ C23×C4×C17 ◁ G | |
1044 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)(20,25)(21,26)(22,31)(23,27)(24,28)(29,32)(30,33)(34,35,38,41)(36,39,43,46)(37,40,44,47)(42,48,49,45);(18,20)(19,24)(21,28)(22,30)(23,29)(25,31)(26,32)(27,33)(34,36)(35,39)(37,42)(38,43)(40,45)(41,46)(44,49)(47,48);(18,20)(19,25)(21,30)(22,28)(23,29)(24,31)(26,33)(27,32)(34,37)(35,40)(36,42)(38,44)(39,45)(41,47)(43,49)(46,48);(18,21,23,22)(19,26,27,31)(20,28,29,30)(24,32,33,25)629 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 11224);