Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C17 · Schur multiplier (H2) = C22 |
| direct product | C17×#8936 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C17 | #120 |
| commutator | C42 | C22×C4×C17 |
| Frattini, cosocle | C2×C42 | C23×C17 |
| socle | C22×C17 | #385 |
| prime radical | C23×C17 | #123 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C17 ◁ C2×C42×C17 ◁ G | |
356 conjugacy classes of subgroups.
| minimal degree | μ(G) = 49 |
| transitive degree | μt(G) = 1088 |
A minimal faithful permutation representation — 3 generators on 49 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17)(19,23)(21,28)(24,32)(25,29)(26,30)(31,33)(34,35,38,42,39,37,46,41)(36,40,44,48,45,43,49,47);(18,19)(20,24)(21,29)(22,25)(23,28)(26,31)(27,33)(30,32)(34,36,38,44,39,45,46,49)(35,40,42,48,37,43,41,47);(18,20,22,27)(19,24,25,33)(21,30,28,26)(23,31,29,32)(34,37)(35,39)(36,43)(38,41)(40,45)(42,46)(44,47)(48,49)884 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 1924);