Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #1366 |
| automorphism | ? |
| homology | Abelianization (H1) = C42×C17 · Schur multiplier (H2) = C22 |
| direct product | C17×#7271 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C17 | #333 |
| commutator | C42 | C42×C17 |
| Frattini, cosocle | C2×C4×C8 | C22×C17 |
| prime radical | C23×C17 | #100 |
| LCS | G ▷ C42 ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C17 ◁ C22×C4×C17 ◁ C2×C4×C8×C17 ◁ G | |
222 conjugacy classes of subgroups.
| minimal degree | μ(G) = 53 |
| transitive degree | μt(G) = 1088 |
A minimal faithful permutation representation — 2 generators on 53 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17)(18,19,20,21)(22,23)(24,32,34,45)(25,37)(26,29)(27,41)(28,33,42,36)(30,40)(31,38)(35,43,49,53)(39,46)(44,51)(47,50,52,48);(22,24,25,35,38,36,51,50,26,34,39,49,27,33,40,48)(23,28,30,43,41,32,46,47,29,42,44,53,31,45,37,52)782 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 259);