Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #23387 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C17 · Schur multiplier (H2) = C23×C4 |
| direct product | C17×#23828 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C17 | C22×D4 |
| commutator, Frattini, cosocle | C22×C4 | C24×C17 |
| prime radical | C2×C17×#127 | C22 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C17 ◁ C17×#376 ◁ G | |
802 conjugacy classes of subgroups.
| minimal degree | μ(G) = 49 |
| transitive degree | μt(G) = 2176 |
A minimal faithful permutation representation — 4 generators on 49 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17)(18,19,22,24)(20,25,21,23)(26,27,29,31)(28,32,33,30)(34,35,37,40)(36,42,44,39)(38,41,46,49)(43,48,45,47);(18,20,22,21)(19,23,24,25)(26,28,29,33)(27,30,31,32)(34,36,37,44)(35,39,40,42)(38,43,46,45)(41,47,49,48);(27,31)(30,32)(36,43)(38,46)(39,47)(41,49)(42,48)(44,45);(18,21,22,20)(19,23,24,25)(35,40)(39,42)(41,49)(47,48)884 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 16816);