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×#61107 |
| 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 | |
2624 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)(20,29)(21,26)(22,38)(23,27)(24,32)(25,36)(28,39)(30,47)(31,46)(33,41)(34,42)(35,43)(37,44)(40,49)(45,48);(18,20,23,34)(19,24,27,41)(21,30,37,49)(22,33,39,32)(25,40,43,47)(26,45,44,46)(28,42,38,29)(31,36,48,35);(18,21)(19,25)(20,30)(22,35)(23,37)(24,40)(26,38)(27,43)(28,44)(29,45)(31,33)(32,48)(34,49)(36,39)(41,47)(42,46);(18,21)(19,26)(20,31)(22,36)(23,37)(24,40)(25,38)(27,44)(28,43)(29,46)(30,33)(32,49)(34,48)(35,39)(41,47)(42,45);(19,27)(24,41)(25,43)(26,44)(28,38)(29,42)(40,47)(45,46)884 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 54095);