Finite Group DatabasebetaFinite Group Databasebeta| order | 8092 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C7⋊#11923876 |
| Fitting, derived, Hall | C7×C289 ⋊ C4 |
| Sylow | C289 ⋊ Dic7 |
| Sylow | C7 ⋊ #11923876 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, hypocenter | C7×C289 | C4 |
| Frattini | C17 | C7⋊#595 |
| socle | C7×C17 | #595 |
| LCS | G ▷ C7×C289 | |
| UCS | C1 | |
18 conjugacy classes of subgroups.
Polycyclic presentation:
2^2,7,17^2|a^2=b,d^17=e^9,c^a=c^6,d^a=d^4e,e^a=e^4,d^b=d^16e^8,e^b=e^16514 conjugacy classes — view the full character table.
| maximal subgroup of | ΓL(1,𝔽8)⋊#11923876, C3×C7⋊#11923876, C3⋊(C7⋊#11923876) |
| maximal normal subgroup of | ΓL(1,𝔽8)⋊#11923876, C3×C7⋊#11923876 |
| maximal quotient of | C3×C7⋊#11923876, C3⋊(C7⋊#11923876) |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8092, 7);