Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #10440 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C17 · Schur multiplier (H2) = C23 |
| direct product | C17×#10446 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C17 | #394 |
| commutator, Frattini, cosocle | C2×C42 | C23×C17 |
| prime radical | C23×C17 | #123 |
| LCS | G ▷ C2×C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C17 ◁ C2×C42×C17 ◁ G | |
408 conjugacy classes of subgroups.
| minimal degree | μ(G) = 57 |
| transitive degree | μt(G) = 2176 |
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)(18,19)(20,22)(21,24)(23,25)(26,27,31,35)(28,36,39,51)(29,40,43,33)(30,44,46,34)(32,45,48,38)(37,53,41,52)(42,50,57,55)(47,54,49,56);(26,28,31,39)(27,32,35,48)(29,41,43,37)(30,45,46,38)(33,49,40,47)(34,51,44,36)(42,54,57,56)(50,52,55,53);(19,22)(20,25)(23,24)(26,29,30,42,31,43,46,57)(27,33,34,50,35,40,44,55)(28,37,38,54,39,41,45,56)(32,47,36,52,48,49,51,53)629 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 3434);