Finite Group DatabasebetaFinite Group Databasebeta| order | 8708 |
| automorphism | Aut(G) order 8098440 |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| dihedral | D4354 |
| direct product | C2×D2177 |
| unambiguous semidirect product | (C2×C7)⋊D311 |
| unambiguous semidirect product | (C2×C311)⋊D7 |
| Fitting, socle | C2×C7×C311 ⋊ C2 |
| derived, Hall | C7×C311 ⋊ C22 |
| Sylow | C311 ⋊ C2×D7 |
| Sylow | C7 ⋊ C2×D311 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | D2177 |
| commutator, hypocenter | C7×C311 | C22 |
| Frattini | C1 | G |
| Fitting, socle | C2×C7×C311 | C2 |
| LCS | G ▷ C7×C311 | |
| UCS | C1 ◁ C2 | |
20 conjugacy classes of subgroups.
2180 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×ΓL(1,𝔽8)⋊D311, D3×D2177, C2×C3×D2177, … |
| maximal normal subgroup of | C2×ΓL(1,𝔽8)⋊D311, C2×C3×D2177, D8708 |
| maximal quotient of | D3×D2177, C2×C3×D2177, C2×D6531, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8708, 7);