Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #10304 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C17 · Schur multiplier (H2) = C23×C4 |
| direct product | C17×#10305 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C17 | #127 |
| commutator, Frattini, cosocle | C2×C42 | C23×C17 |
| prime radical | C2×C17×#493 | C2 |
| LCS | G ▷ C2×C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C23×C17 ◁ C2×C42×C17 ◁ G | |
802 conjugacy classes of subgroups.
| minimal degree | μ(G) = 37 |
| transitive degree | μt(G) = 2176 |
A minimal faithful permutation representation — 3 generators on 37 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17)(18,19)(20,21)(22,23,26,24)(25,28,27,29)(30,31,34,37)(32,35,33,36);(19,21)(23,28)(24,29)(25,27)(31,35)(32,33)(36,37);(22,24)(23,26)(25,29)(27,28)(31,36)(32,33)(35,37)884 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 3293);