Finite Group DatabasebetaFinite Group Databasebeta| order | 10983 |
| automorphism | ? |
| homology | Abelianization (H1) = C3 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Fitting, socle, derived, Hall | C7×C523 ⋊ C3 |
| Sylow | C523 ⋊ ΓL(1,𝔽8) |
| Sylow | C7 ⋊ C523⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C7×C523 | C3 |
| LCS | G ▷ C7×C523 | |
| UCS | C1 | |
8 conjugacy classes of subgroups.
Polycyclic presentation:
3,7,523|b^a=b^2,c^a=c^601223 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×#24926886, #36346974, #36346978, … |
| maximal normal subgroup of | C2×#24926886, #36346974, #36346978, … |
| maximal quotient of | C2×#24926886, #45682000, C3×#24926886 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10983, 3);