Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C17 · Schur multiplier (H2) = C24 |
| direct product | C17×#19435 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C17 | C2×#121 |
| commutator, Frattini, cosocle | C42 | C24×C17 |
| prime radical | C23×C17 | #121 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C17 ◁ C2×C42×C17 ◁ G | |
582 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)(18,19,22,25)(20,26,28,33)(21,30,27,24)(23,31,32,29)(36,42)(37,44)(39,46)(41,48)(43,45)(47,49);(18,20,27,31,22,28,21,29)(19,23,30,33,25,32,24,26)(34,35)(36,39)(37,41)(38,40)(42,46)(43,47)(44,48)(45,49);(20,28)(23,32)(26,33)(29,31)(34,36,38,43)(35,39,40,47)(37,45,44,42)(41,49,48,46);(35,40)(39,47)(41,48)(46,49)629 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 12423);