Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #62636 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C17 · Schur multiplier (H2) = C29 |
| direct product | C17×#62636 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C17 | C23×D8 |
| commutator, Frattini, cosocle | C8 | C25×C17 |
| LCS | G ▷ C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C17 ◁ C2×#41×C17 ◁ C2×C17×#131 ◁ G | |
2078 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)(20,25)(21,24)(22,35)(23,26)(27,32)(28,33)(29,39)(30,36)(31,45)(34,37)(38,46)(40,44)(41,43)(42,47)(48,49);(19,24)(21,32)(22,33)(25,36)(26,37)(27,28)(30,44)(31,43)(34,46)(35,38)(39,47)(40,41)(42,49)(45,48);(18,20)(19,25)(21,30)(22,31)(23,29)(24,36)(26,39)(27,40)(28,41)(32,44)(33,43)(34,42)(35,45)(37,47)(38,48)(46,49);(20,29)(25,39)(30,42)(31,43)(36,47)(40,48)(41,45)(44,49);(19,26)(24,37)(25,39)(27,38)(28,35)(36,47)(40,48)(41,45)986 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 55624);