Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #33856 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C17 · Schur multiplier (H2) = C25 |
| direct product | C17×#33858 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C17 | D4×D8 |
| commutator, Frattini, cosocle | C2×C8 | C24×C17 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C17 ◁ C2×C4×C17 ◁ C17×#443 ◁ G | |
668 conjugacy classes of subgroups.
| minimal degree | μ(G) = 49 |
| transitive degree | μt(G) = 544 |
A minimal faithful permutation representation — 4 generators on 49 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17)(19,25)(20,30)(21,34)(22,23)(26,27)(28,44)(29,43)(31,48)(32,46)(33,39)(35,40)(37,38)(41,42)(45,47);(18,19,24,29)(20,31,33,26)(21,35,38,44)(22,28,23,40)(25,37,43,34)(27,46,48,32)(30,45,39,42)(36,47,49,41);(18,20)(19,26)(21,32)(22,39)(23,30)(24,33)(25,41)(27,44)(28,45)(29,31)(34,36)(35,48)(37,49)(38,46)(40,42)(43,47);(18,20)(19,27)(21,36)(22,30)(23,39)(24,33)(25,42)(26,44)(28,47)(29,48)(31,35)(32,34)(37,46)(38,49)(40,41)(43,45)731 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 26846);