Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 2 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C17 · Schur multiplier (H2) = C27 |
| direct product | C17×#36798 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C17 | C25 |
| commutator, Frattini, cosocle | C23 | C25×C17 |
| prime radical | C22×D4×C17 | C23 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C23×C17 ◁ G | |
1518 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)(20,24)(23,25)(28,32)(31,33)(34,35,39,40)(36,43,46,41)(37,47,42,38)(44,45,48,49);(19,22)(23,25)(26,27,30,29)(28,31,32,33)(35,40)(37,42)(41,43)(44,48);(18,19)(20,23)(21,22)(24,25)(26,28)(27,31)(29,33)(30,32)(34,36,39,46)(35,41,40,43)(37,44,42,48)(38,45,47,49);(18,19)(20,23)(21,22)(24,25)(26,29,30,27)(28,33,32,31)(34,37,39,42)(35,38,40,47)(36,44,46,48)(41,45,43,49);(18,20)(19,23)(21,24)(22,25)(34,38)(35,42)(36,45)(37,40)(39,47)(41,48)(43,44)(46,49)884 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 29786);