Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #18414 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C17 · Schur multiplier (H2) = C25 |
| direct product | C17×#18442 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C17 | C2×#120 |
| commutator, Frattini, cosocle | C22×C4 | C24×C17 |
| prime radical | C17×#121 | C23 |
| LCS | G ▷ C22×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C17 ◁ C2×C42×C17 ◁ G | |
848 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)(19,23)(21,28)(24,30)(25,29)(27,32)(31,33)(34,35,40,37)(36,44,47,49)(38,43,39,42)(41,48,45,46);(18,19,22,25)(20,24,26,31)(21,29,28,23)(27,33,32,30)(34,36,40,47)(35,41,37,45)(38,46,39,48)(42,44,43,49);(18,20,22,26)(19,24,25,31)(21,27,28,32)(23,30,29,33)(34,37,40,35)(36,45,47,41)(38,42,39,43)(44,48,49,46);(20,26)(24,31)(27,32)(30,33)(34,38,40,39)(35,42,37,43)(36,46,47,48)(41,44,45,49)629 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 11430);