Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C17 · Schur multiplier (H2) = C2×C4 |
| direct product | C17×#8824 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C17 | #127 |
| commutator | C42 | C22×C4×C17 |
| Frattini, cosocle | C2×C42 | C23×C17 |
| socle | C22×C17 | #384 |
| prime radical | C23×C17 | C4⋊Q8 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C17 ◁ C2×C42×C17 ◁ G | |
322 conjugacy classes of subgroups.
| minimal degree | μ(G) = 49 |
| transitive degree | μt(G) = 2176 |
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)(18,19,22,25,23,26,21,31)(20,27,29,32,30,33,28,24)(34,35)(36,42)(37,39)(38,46)(40,44)(41,45)(43,48)(47,49);(18,20,21,28,23,30,22,29)(19,24,25,27,26,32,31,33)(35,39)(40,47)(41,46)(42,48);(34,36,38,44,37,43,45,49)(35,40,41,42,39,47,46,48)1292 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 1812);