Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 2 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C17 · Schur multiplier (H2) = C25×C4 |
| direct product | C17×#15143 |
| subgroup | G/H | |
|---|---|---|
| center, socle, prime radical | C24×C17 | C24 |
| commutator, Frattini, cosocle | C24 | C24×C17 |
| LCS | G ▷ C24 ▷ C1 | |
| UCS | C1 ◁ C24×C17 ◁ G | |
1934 conjugacy classes of subgroups.
| minimal degree | μ(G) = 37 |
| transitive degree | μt(G) = 4352 |
A minimal faithful permutation representation — 4 generators on 37 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17)(19,21)(23,24)(30,31,34,37)(32,36,33,35);(27,29)(30,32,34,33)(31,35,37,36);(22,23,25,24)(26,27)(28,29);(18,19,20,21)(22,24,25,23)(30,33,34,32)(31,36,37,35)1088 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 8131);