Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 2 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C17 · Schur multiplier (H2) = C22×C4 |
| direct product | C17×#21436 |
| subgroup | G/H | |
|---|---|---|
| center | C22×C4×C17 | C24 |
| commutator | C23 | C23×C4×C17 |
| Frattini, cosocle | C22×C4 | C24×C17 |
| socle | C23×C17 | C23×C4 |
| prime radical | C24×C17 | C22×C4 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C22×C4×C17 ◁ G | |
688 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)(20,23)(21,22)(24,25)(26,27)(28,31)(29,30)(32,33)(34,35,39,36,38,41,46,43)(37,40,45,42,44,47,49,48);(19,22)(23,25)(34,36,39,41,38,43,46,35)(37,42,45,47,44,48,49,40);(18,20,21,24)(19,23,22,25)(27,30)(31,33)(34,37,38,44)(35,40,41,47)(36,42,43,48)(39,45,46,49);(26,28,29,32)(27,31,30,33)(37,44)(40,47)(42,48)(45,49)1292 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 14424);