Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 4 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C17 · Schur multiplier (H2) = C22 |
| direct product | C17×#13187 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C17 | #476 |
| commutator | C2×C8 | C22×C4×C17 |
| Frattini, cosocle | C22×C8 | C23×C17 |
| prime radical | C23×C17 | AGL(1,ℤ/8) |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C17 ◁ C22×C4×C17 ◁ C2×C4×C8×C17 ◁ G | |
294 conjugacy classes of subgroups.
| minimal degree | μ(G) = 53 |
| transitive degree | μt(G) = 1088 |
A minimal faithful permutation representation — 3 generators on 53 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17)(19,21)(22,23)(24,34,38,52)(25,40)(26,30)(27,45)(28,33)(29,36,47,35)(31,42)(32,41)(37,50,39,51)(43,48,53,46)(44,49);(22,24,27,37,28,38,41,39)(23,29,32,46,33,47,45,48)(25,35,26,43,42,36,44,53)(30,34,40,51,49,52,31,50);(18,19,20,21)(22,25,41,44,28,42,27,26)(23,30,45,31,33,49,32,40)(24,35,39,53,38,36,37,43)(29,34,48,50,47,52,46,51)782 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 6175);