Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #1714 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C17 · Schur multiplier (H2) = C23×C4 |
| direct product | C2×C17×#1723 |
| subgroup | G/H | |
|---|---|---|
| center, socle, prime radical | C23×C17 | #127 |
| commutator, Frattini, cosocle | C42 | C24×C17 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C23×C17 ◁ C2×C42×C17 ◁ G | |
798 conjugacy classes of subgroups.
| minimal degree | μ(G) = 43 |
| transitive degree | μt(G) = 4352 |
A minimal faithful permutation representation — 4 generators on 43 points:
(1,2)(27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43);(4,7)(5,9)(8,10)(11,12,15,18)(13,19,22,26)(14,23,20,17)(16,24,25,21);(3,4,5,7,6,8,9,10);(4,8)(7,10)(11,13,20,24,15,22,14,21)(12,16,23,26,18,25,17,19)884 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 12605);