Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C17 · Schur multiplier (H2) = C25 |
| direct product | C17×#19009 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C17 | C2×#120 |
| commutator, Frattini, cosocle | C42 | C24×C17 |
| prime radical | C17×#3531 | C2 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C17 ◁ C2×C42×C17 ◁ G | |
832 conjugacy classes of subgroups.
| minimal degree | μ(G) = 49 |
| transitive degree | μt(G) = 2176 |
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)(20,28)(21,22)(26,27)(29,30)(31,32)(34,35,39,36)(37,44,45,49)(38,43,48,41)(40,47,42,46);(18,19)(20,25)(21,26)(22,24)(23,27)(28,32)(29,33)(30,31)(34,36,39,35)(37,42,45,40)(38,41,48,43)(44,47,49,46);(18,20)(19,25)(21,28)(22,30)(23,29)(24,31)(26,32)(27,33)(34,37)(35,40)(36,42)(38,47)(39,45)(41,49)(43,44)(46,48);(18,21,23,22)(19,26,27,24)(20,28,29,30)(25,32,33,31)578 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 11997);