Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C17 · Schur multiplier (H2) = C29 |
| direct product | C17×#61105 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C17 | D42 |
| commutator, Frattini, cosocle | C2×C4 | C25×C17 |
| socle | C2×C17 | C2×D42 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C17 ◁ C22×C4×C17 ◁ G | |
2620 conjugacy classes of subgroups.
| minimal degree | μ(G) = 49 |
| transitive degree | μt(G) = 544 |
A minimal faithful permutation representation — 5 generators on 49 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17)(18,19)(20,30)(21,32)(22,27)(23,28)(24,41)(25,29)(26,35)(31,47)(33,36)(34,48)(37,49)(38,44)(39,45)(40,46)(42,43);(18,20)(19,21)(22,37)(23,32)(24,33)(25,26)(27,43)(28,35)(29,36)(30,41)(31,38)(34,45)(39,42)(40,48)(44,49)(46,47);(18,21)(19,26)(20,29)(22,34)(23,35)(24,30)(25,36)(27,42)(28,33)(31,46)(32,41)(37,44)(38,43)(39,47)(40,49)(45,48);(18,22)(19,27)(20,31)(21,34)(23,38)(24,39)(25,40)(26,42)(28,44)(29,46)(30,47)(32,48)(33,37)(35,43)(36,49)(41,45);(18,23,25,24)(19,28,29,41)(20,32,26,33)(21,35,36,30)(22,38,40,39)(27,44,46,45)(31,48,42,37)(34,43,49,47)986 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 54093);