Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 2 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C17 · Schur multiplier (H2) = C27 |
| direct product | C17×#36676 |
| 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 | |
2006 conjugacy classes of subgroups.
| minimal degree | μ(G) = 41 |
| transitive degree | μt(G) = 1088 |
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)(18,19,21,22)(20,23,24,25)(26,27)(28,31)(29,30)(32,33)(34,35,37,39)(36,40,41,38);(19,22)(23,25)(34,36)(35,38)(37,41)(39,40);(18,20)(19,23)(21,24)(22,25)(27,30)(31,33)(36,41)(38,40);(20,24)(23,25)(35,39)(38,40);(26,28,29,32)(27,31,30,33)884 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 29664);