Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 2 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C17 · Schur multiplier (H2) = C27×C4 |
| direct product | C17×#36703 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C17 | C25 |
| commutator, Frattini, cosocle | C23 | C25×C17 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C23×C17 ◁ G | |
4062 conjugacy classes of subgroups.
| minimal degree | μ(G) = 37 |
| transitive degree | μt(G) = 544 |
A minimal faithful permutation representation — 5 generators on 37 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17)(19,21)(23,26)(24,28)(32,36)(35,37);(22,23,25,26)(24,27,28,29)(31,34)(35,37);(18,19)(20,21)(30,31)(32,35)(33,34)(36,37);(22,23)(24,27)(25,26)(28,29)(30,31)(32,35)(33,34)(36,37);(22,24)(23,27)(25,28)(26,29)(30,32)(31,35)(33,36)(34,37)884 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 29691);