Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C17 · Schur multiplier (H2) = C24 |
| direct product | C17×#19423 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C17 | C2×#121 |
| commutator, Frattini, cosocle | C42 | C24×C17 |
| prime radical | C22×D4×C17 | D4 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C17 ◁ C2×C42×C17 ◁ G | |
630 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)(18,19,22,25)(20,26,28,33)(21,30,27,24)(23,31,32,29)(34,35)(36,39)(37,40)(38,42)(41,45)(43,47)(44,46)(48,49);(18,20,27,31,22,28,21,29)(19,23,30,33,25,32,24,26)(34,36)(35,39)(37,44)(38,43)(40,46)(41,48)(42,47)(45,49);(20,28)(23,32)(26,33)(29,31)(35,40)(37,45)(39,46)(41,42)(44,49)(47,48);(36,43)(39,47)(44,49)(46,48)629 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 12411);