Finite Group DatabasebetaFinite Group Databasebeta| order | 13712 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C22 |
| unambiguous semidirect product | C22⋊Dic857 |
| Sylow | C857 ⋊ C22⋊C4 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C2×D857 |
| commutator | C2×C857 | C2×C4 |
| Fitting, prime radical | C23×C857 | C2 |
| socle, cosocle | C22×C857 | C22 |
| hypercenter | C23 | D857 |
| hypocenter | C857 | C22⋊C4 |
| LCS | G ▷ C2×C857 ▷ C857 | |
| UCS | C1 ◁ C22 ◁ C23 | |
34 conjugacy classes of subgroups.
| transitive degree | μt(G) = 6856 |
Polycyclic presentation:
2^4,857|a^2=d,b^a=bc,e^a=e^8563434 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #42116743, #42116744, C22⋊C4×D857, … |
| maximal normal subgroup of | #42116743, #42116744, C22⋊C4×D857, … |
| maximal quotient of | #42116736, C22⋊#20293507, #42116744, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13712, 18);