Finite Group DatabasebetaFinite Group Databasebeta| order | 16136 |
| automorphism | ? |
| homology | Abelianization (H1) = C8 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Fitting, socle, derived, Sylow | C2017 ⋊ C8 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C2017 | C8 |
| prime radical | D2017 | C4 |
| cosocle | #22549029 | C2 |
| LCS | G ▷ C2017 | |
| UCS | C1 | |
8 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2017 |
Polycyclic presentation:
2^3,2017|a^2=b,b^2=c,d^a=d^1579,d^b=d^229,d^c=d^2016260 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#30633241, #44567645 |
| maximal normal subgroup of | C2×#30633241, #44567645 |
| maximal quotient of | #44567643, C2×#30633241 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(16136, 15);