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×#33965 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C17 | C22×D8 |
| commutator, Frattini, cosocle | C2×C8 | C24×C17 |
| prime radical | C2×D8×C17 | C23 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C17 ◁ C4×Q8×C17 ◁ C8×Q8×C17 ◁ G | |
498 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)(26,27,31,36)(28,32,37,47)(29,33,42,50)(30,43,41,35)(34,51,49,40)(38,48,52,44)(39,56,53,46)(45,54,57,55);(18,19,22,23)(20,24,21,25)(26,28)(27,32)(29,38)(30,39)(31,37)(33,48)(34,45)(35,46)(36,47)(40,55)(41,53)(42,52)(43,56)(44,50)(49,57)(51,54);(18,20,22,21)(19,24,23,25)(27,33)(28,37)(29,40)(30,41)(32,44)(34,35)(36,50)(38,54)(42,51)(43,49)(45,56)(46,57)(47,48)(52,55);(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, 26953);