Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C17 · Schur multiplier (H2) = C4 |
| direct product | C17×#9893 |
| subgroup | G/H | |
|---|---|---|
| center, socle, prime radical | C23×C17 | C2×C22⋊C4 |
| commutator | C22×C4 | C22×C4×C17 |
| Frattini, cosocle | C2×C42 | C23×C17 |
| LCS | G ▷ C22×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C23×C17 ◁ C43×C17 ◁ G | |
388 conjugacy classes of subgroups.
| minimal degree | μ(G) = 49 |
| transitive degree | μt(G) = 4352 |
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)(18,19)(20,24)(21,22)(23,25)(27,30,31,32)(34,35,38,41,39,42,37,47)(36,43,46,48,44,49,45,40);(19,22)(23,24)(26,27,28,32,29,31,33,30)(34,36)(35,40,42,48)(37,45)(38,46)(39,44)(41,43,47,49);(18,20,21,25)(19,23,22,24)(36,44)(40,48)(43,49)(45,46)782 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 2881);