Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #10046 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C17 · Schur multiplier (H2) = C22 |
| direct product | C17×#10422 |
| subgroup | G/H | |
|---|---|---|
| center, socle, prime radical | C23×C17 | #120 |
| commutator, Frattini, cosocle | C2×C42 | C23×C17 |
| LCS | G ▷ C2×C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C23×C17 ◁ C2×C42×C17 ◁ G | |
452 conjugacy classes of subgroups.
| minimal degree | μ(G) = 37 |
| transitive degree | μt(G) = 4352 |
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)(19,20)(22,23,26,29)(24,27,25,28)(30,31)(32,33)(34,36)(35,37);(18,19)(20,21)(22,24,26,25)(23,27,29,28)(30,32,35,36)(31,33,37,34);(18,20,21,19)(23,28)(24,25)(27,29)(31,32)(33,34)(36,37)782 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 3410);