Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #61106 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C17 · Schur multiplier (H2) = C29 |
| direct product | C17×#61106 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C17 | C2×D42 |
| commutator, Frattini, cosocle | C2×C4 | C25×C17 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C17 ◁ C22×C4×C17 ◁ G | |
2656 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)(20,31)(21,27)(22,30)(23,29)(24,28)(25,34)(26,36)(32,40)(33,47)(35,46)(37,45)(38,42)(39,43)(41,49)(44,48);(18,20)(19,25)(21,32)(22,38)(23,34)(24,35)(26,40)(27,44)(28,42)(29,46)(30,31)(33,36)(37,49)(39,48)(41,43)(45,47);(18,21)(19,26)(20,32)(22,36)(23,39)(24,37)(25,40)(27,29)(28,43)(30,45)(31,47)(33,38)(34,48)(35,49)(41,42)(44,46);(18,21)(19,27)(20,33)(22,39)(23,36)(24,37)(25,41)(26,29)(28,45)(30,43)(31,47)(32,38)(34,49)(35,48)(40,42)(44,46);(19,28)(25,42)(26,43)(27,45)(29,30)(31,46)(40,41)(44,47)884 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 54094);