Finite Group DatabasebetaFinite Group Databasebeta| order | 17031 |
| automorphism | ? |
| homology | Abelianization (H1) = C3 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Fitting, socle, derived, Hall | C7×C811 ⋊ C3 |
| Sylow | C811 ⋊ ΓL(1,𝔽8) |
| Sylow | C7 ⋊ C811⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C7×C811 | C3 |
| LCS | G ▷ C7×C811 | |
| UCS | C1 | |
8 conjugacy classes of subgroups.
| transitive degree | μt(G) = 5677 |
Polycyclic presentation:
3,7,811|b^a=b^2,c^a=c^1301895 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×#30684604, #46801585, #46801589, … |
| maximal normal subgroup of | C2×#30684604, #46801585, #46801589, … |
| maximal quotient of | C2×#30684604 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17031, 3);