Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C17 · Schur multiplier (H2) = C28 |
| direct product | C17×#61909 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C17 | C23×D4 |
| commutator, Frattini, cosocle | C2×C4 | C25×C17 |
| prime radical | C17×#3480 | C2 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C17 ◁ C2×C4×Q8×C17 ◁ G | |
1710 conjugacy classes of subgroups.
| minimal degree | μ(G) = 49 |
| transitive degree | μt(G) = 2176 |
A minimal faithful permutation representation — 5 generators on 49 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17)(18,19)(20,28)(21,25)(22,26)(23,27)(24,30)(29,33)(31,32)(34,35,38,42)(36,43,39,40)(37,45,46,49)(41,47,48,44);(18,20,23,30)(19,24,27,28)(21,29,22,31)(25,32,26,33)(34,36,38,39)(35,40,42,43)(37,44,46,47)(41,45,48,49);(18,21,23,22)(19,25,27,26)(20,29,30,31)(24,32,28,33)(34,37,38,46)(35,41,42,48)(36,44,39,47)(40,45,43,49);(18,22,23,21)(19,26,27,25)(20,29,30,31)(24,32,28,33);(19,27)(24,28)(25,26)(32,33)(34,36,38,39)(35,40,42,43)(37,44,46,47)(41,45,48,49)884 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 54897);