Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C17 · Schur multiplier (H2) = C25 |
| direct product | C17×#19059 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C17 | C2×#120 |
| commutator, Frattini, cosocle | C42 | C24×C17 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C17 ◁ C2×C42×C17 ◁ G | |
898 conjugacy classes of subgroups.
| minimal degree | μ(G) = 49 |
| transitive degree | μt(G) = 1088 |
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)(19,24)(20,27)(21,22)(26,29)(28,30)(31,33)(35,39)(37,44)(40,48)(41,45)(43,46)(47,49);(18,19)(20,25)(21,29)(22,24)(23,26)(27,33)(28,32)(30,31)(34,35,38,41)(36,40,42,49)(37,45,44,39)(43,47,46,48);(18,20)(19,25)(21,27)(22,30)(23,28)(24,31)(26,32)(29,33)(34,36)(35,40)(37,46)(38,42)(39,47)(41,49)(43,44)(45,48);(20,28)(25,32)(27,30)(31,33)(36,42)(40,49)(43,46)(47,48)578 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 12047);