Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C8×C17 · Schur multiplier (H2) = C22×C8 |
| direct product | C17×#8156 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C8×C17 | C22⋊C4 |
| commutator | C22 | C2×C4×C8×C17 |
| Frattini, cosocle | C2×C42 | C23×C17 |
| socle | C22×C17 | C4×C22⋊C4 |
| prime radical | C24×C17 | C42 |
| LCS | G ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C8×C17 ◁ C2×C4×C8×C17 ◁ G | |
506 conjugacy classes of subgroups.
| minimal degree | μ(G) = 57 |
| transitive degree | μt(G) = 1088 |
A minimal faithful permutation representation — 3 generators on 57 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17)(26,27,30,34,31,35,42,48)(28,36,39,50,38,32,43,45)(29,33,40,46,41,47,53,56)(37,49,52,57,51,44,54,55);(18,19,20,22,21,23,24,25)(26,28)(27,32,35,36)(29,37)(30,39)(31,38)(33,44,47,49)(34,45,48,50)(40,52)(41,51)(42,43)(46,55,56,57)(53,54);(26,29,30,40,31,41,42,53)(27,33,34,46,35,47,48,56)(28,37,39,52,38,51,43,54)(32,44,45,55,36,49,50,57)1496 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 1144);