Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #10464 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C17 · Schur multiplier (H2) = C22 |
| direct product | C17×#10471 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C17 | #394 |
| commutator, Frattini, cosocle | C2×C42 | C23×C17 |
| prime radical | C23×C17 | #121 |
| LCS | G ▷ C2×C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C17 ◁ C2×C42×C17 ◁ G | |
366 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)(18,19,20,22)(21,23,25,24)(26,27)(28,37)(29,42)(30,47)(31,35)(32,36)(33,39)(34,45)(38,53)(40,49)(41,52)(43,48)(44,51)(46,56)(50,55)(54,57);(19,22)(23,24)(26,28,32,41)(27,33,36,49)(29,43,45,54)(30,40,31,39)(34,50,42,53)(35,52,47,37)(38,44,55,46)(48,56,57,51);(19,23)(21,25)(22,24)(26,29,30,44,32,45,31,46)(27,34,35,51,36,42,47,56)(28,38,39,54,41,55,40,43)(33,48,37,50,49,57,52,53)629 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 3459);