Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C17 · Schur multiplier (H2) = C25 |
| direct product | C17×#19010 |
| 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 | |
920 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)(18,19)(20,28)(21,27)(22,26)(23,25)(24,29)(30,33)(31,32)(35,40)(37,38)(41,48)(42,45)(43,46)(47,49);(18,20)(19,24)(21,31)(22,29)(23,30)(25,32)(26,33)(27,28)(34,35)(36,41)(37,40)(38,45)(39,42)(43,47)(44,49)(46,48);(18,20)(19,24)(21,29)(22,31)(23,30)(25,32)(26,28)(27,33)(34,36)(35,41)(37,43)(38,46)(39,44)(40,47)(42,49)(45,48);(19,25)(24,32)(26,27)(28,33)(34,37,39,38)(35,40,42,45)(36,43,44,46)(41,47,49,48)578 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 11998);