Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 2 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C17 · Schur multiplier (H2) = C27 |
| direct product | C17×#36851 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C17 | C25 |
| commutator, Frattini, cosocle | C23 | C25×C17 |
| prime radical | C17×#2671 | C2 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C23×C17 ◁ G | |
1664 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)(20,24)(23,25)(26,27)(28,33)(29,31)(30,32)(35,38)(39,41);(19,22)(23,25)(27,29)(32,33);(18,19)(20,23)(21,22)(24,25)(26,28,31,30)(27,32,29,33)(34,35)(36,39)(37,38)(40,41);(18,19)(20,23)(21,22)(24,25)(26,29,31,27)(28,33,30,32);(18,20)(19,23)(21,24)(22,25)(26,30,31,28)(27,33,29,32)(34,36,37,40)(35,39,38,41)884 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 29839);