Finite Group DatabasebetaFinite Group Databasebeta| order | 13712 |
| automorphism | ? |
| homology | Abelianization (H1) = C16 · Schur multiplier (H2) = C1 |
No aliases for this group.
| derived, Sylow | C857 ⋊ C16 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C8 | D857 |
| commutator, hypocenter | C857 | C16 |
| Fitting, cosocle | C8×C857 | C2 |
| socle, prime radical | C2×C857 | C8 |
| LCS | G ▷ C857 | |
| UCS | C1 ◁ C8 | |
10 conjugacy classes of subgroups.
| transitive degree | μt(G) = 13712 |
Polycyclic presentation:
2^4,857|a^2=b,b^2=c,c^2=d,e^a=e^8563440 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C16×D857, C2×#28351404, #42116768, … |
| maximal normal subgroup of | C16×D857, C2×#28351404, #42116768, … |
| maximal quotient of | #42116735, C2×#28351404 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13712, 15);