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×#33967 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C17 | C22×D8 |
| commutator, Frattini, cosocle | C2×C8 | C24×C17 |
| prime radical | C17×#493 | C22 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C17 ◁ C4×Q8×C17 ◁ C8×Q8×C17 ◁ G | |
510 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)(19,23)(24,25)(26,27,31,35)(28,36,37,54)(29,40,44,55)(30,45,42,34)(32,47,48,38)(33,50,52,43)(39,56,46,51)(41,53,57,49);(18,19,22,23)(20,24,21,25)(28,37)(32,48)(36,54)(38,47)(39,46)(41,57)(49,53)(51,56);(18,20,22,21)(19,24,23,25)(26,28,31,37)(27,32,35,48)(29,41,44,57)(30,46,42,39)(33,51,52,56)(34,53,45,49)(36,55,54,40)(38,50,47,43);(18,21,22,20)(19,24,23,25)731 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 26955);