Finite Group DatabasebetaFinite Group Databasebeta| order | 8092 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C7⋊#11923885 |
| Fitting, socle, derived, Hall | C7×C172 ⋊ C4 |
| Sylow | C172 ⋊ Dic7 |
| Sylow | C7 ⋊ #11923885 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C7×C172 | C4 |
| LCS | G ▷ C7×C172 | |
| UCS | C1 | |
32 conjugacy classes of subgroups.
Polycyclic presentation:
2^2,7,17^2|a^2=b,c^a=c^6,d^a=d^13,e^a=e^16,d^b=d^16598 conjugacy classes — view the full character table.
| maximal subgroup of | ΓL(1,𝔽8)⋊#11923885, C3×C7⋊#11923885, C3⋊(C7⋊#11923885) |
| maximal normal subgroup of | ΓL(1,𝔽8)⋊#11923885, C3×C7⋊#11923885 |
| maximal quotient of | C3×C7⋊#11923885, C3⋊(C7⋊#11923885) |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8092, 28);