Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #33830 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C17 · Schur multiplier (H2) = C24 |
| direct product | C17×#33900 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C17 | C22×D8 |
| commutator, Frattini, cosocle | C2×C8 | C24×C17 |
| prime radical | C17×#3287 | C2 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C17 ◁ C4×D4×C17 ◁ C8×D4×C17 ◁ G | |
558 conjugacy classes of subgroups.
| minimal degree | μ(G) = 57 |
| transitive degree | μt(G) = 2176 |
A minimal faithful permutation representation — 4 generators on 57 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17)(18,19,21,23)(20,24,25,22)(26,27,32,37)(28,38,39,55)(29,36,31,34)(30,43,46,51)(33,48,49,41)(35,42,53,45)(40,56,47,52)(44,54,57,50);(18,20)(19,22)(21,25)(23,24)(28,39)(33,49)(38,55)(40,47)(41,48)(44,57)(50,54)(52,56);(26,28,32,39)(27,33,37,49)(29,40,31,47)(30,44,46,57)(34,50,36,54)(35,52,53,56)(38,51,55,43)(41,42,48,45);(20,25)(22,24)(26,29,32,31)(27,34,37,36)(28,40,39,47)(30,42,46,45)(33,50,49,54)(35,51,53,43)(38,52,55,56)(41,44,48,57)731 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 26888);