Finite Group DatabasebetaFinite Group Databasebeta| order | 13712 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C2 |
No aliases for this group.
| derived, Sylow | C857 ⋊ C2×C8 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C4 | #16812170 |
| commutator, hypocenter | C857 | C2×C8 |
| Frattini | C2 | C2×#16812170 |
| Fitting | C4×C857 | C4 |
| socle | C2×C857 | C2×C4 |
| prime radical | C2×D857 | C4 |
| cosocle | Dic857 | C22 |
| LCS | G ▷ C857 | |
| UCS | C1 ◁ C4 | |
22 conjugacy classes of subgroups.
| transitive degree | μt(G) = 6856 |
Polycyclic presentation:
2^4,857|a^2=c,c^2=d,e^a=e^207,e^b=e^856,e^c=e^856872 conjugacy classes — view the full character table.
| maximal subgroup of | C8×#16812170, #42116883, #42116891, … |
| maximal normal subgroup of | C8×#16812170, #42116883, #42116891, … |
| maximal quotient of | C4×#20293514, #42116886, #42116896, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13712, 48);