Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 4 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C17 · Schur multiplier (H2) = C22 |
| direct product | C17×#13188 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C17 | #476 |
| commutator | C2×C8 | C22×C4×C17 |
| Frattini, cosocle | C22×C8 | C23×C17 |
| socle | C2×C17 | #1948 |
| prime radical | C23×C17 | #137 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C17 ◁ C22×C4×C17 ◁ C2×C4×C8×C17 ◁ G | |
280 conjugacy classes of subgroups.
| minimal degree | μ(G) = 49 |
| transitive degree | μt(G) = 544 |
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)(18,19,23,30,25,31,24,29)(20,32,36,46,37,43,35,49)(21,38,39,27,40,28,22,41)(26,42,44,34,45,48,47,33);(18,20)(19,26,31,45)(21,33)(22,42)(23,35)(24,36)(25,37)(27,43,41,32)(28,46,38,49)(29,44,30,47)(34,40)(39,48);(18,21,23,39,25,40,24,22)(19,27,29,38,31,41,30,28)(20,33,35,48,37,34,36,42)(26,43,44,49,45,32,47,46)782 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 6176);