Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 2 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C17 · Schur multiplier (H2) = C27 |
| direct product | C17×#36772 |
| 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 | |
1494 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)(30,33)(34,35,39,40)(36,41,43,38)(37,45,47,42)(44,46,49,48);(19,22)(23,25)(26,27,29,31)(28,30,32,33)(35,40)(36,43)(42,45)(44,49);(18,19)(20,23)(21,22)(24,25)(26,28,29,32)(27,30,31,33)(34,36)(35,41)(37,44)(38,40)(39,43)(42,48)(45,46)(47,49);(18,19)(20,23)(21,22)(24,25)(34,37,39,47)(35,42,40,45)(36,44,43,49)(38,46,41,48);(18,20)(19,23)(21,24)(22,25)(34,38,39,41)(35,36,40,43)(37,46,47,48)(42,44,45,49)884 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 29760);