Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 2 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C17 · Schur multiplier (H2) = C27 |
| direct product | C17×#36670 |
| subgroup | G/H | |
|---|---|---|
| center | C22×C4×C17 | C24 |
| commutator, Frattini, cosocle | C23 | C25×C17 |
| socle | C23×C17 | C25 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C22×C4×C17 ◁ G | |
1794 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)(18,19,21,23)(20,22,24,25)(26,27)(28,30)(29,31)(32,33)(34,35)(36,40)(37,41)(38,39)(42,45)(43,47)(44,46)(48,49);(18,20,21,24)(19,22,23,25)(28,32)(30,33)(35,39)(40,45)(41,46)(47,49);(19,23)(22,25)(26,28)(27,30)(29,32)(31,33)(34,36)(35,40)(37,43)(38,42)(39,45)(41,47)(44,48)(46,49);(27,31)(28,32)(36,42)(40,45)(43,48)(47,49);(34,37,38,44)(35,41,39,46)(36,43,42,48)(40,47,45,49)884 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 29658);