Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 2 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C17 · Schur multiplier (H2) = C27 |
| direct product | C17×#36835 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C17 | C25 |
| commutator, Frattini, cosocle | C23 | C25×C17 |
| prime radical | C2×C17×#121 | C22 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C23×C17 ◁ G | |
1610 conjugacy classes of subgroups.
| minimal degree | μ(G) = 41 |
| transitive degree | μt(G) = 2176 |
A minimal faithful permutation representation — 5 generators on 41 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17)(19,21)(20,24)(28,32)(31,33)(36,40)(39,41);(18,19,22,21)(20,25,24,23)(27,30)(31,33)(34,35,38,37)(36,39,40,41);(26,27)(28,31)(29,30)(32,33)(34,36,38,40)(35,39,37,41);(18,20,22,24)(19,23,21,25)(26,27)(28,31)(29,30)(32,33)(34,37,38,35)(36,41,40,39);(18,21,22,19)(20,25,24,23)(26,28)(27,31)(29,32)(30,33)884 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 29823);