Finite Group DatabasebetaFinite Group Databasebeta| order | 7917 |
| isoclinism | isoclinic class of #63270 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C29 · Schur multiplier (H2) = C1 |
| direct product | C29×#63270 |
| Fitting, socle, Hall | C7×C13×C29 ⋊ C3 |
| derived, Hall | C7×C13 ⋊ C3×C29 |
| Hall | C13×C29 ⋊ ΓL(1,𝔽8) |
| Hall | C7×C29 ⋊ C13⋊C3 |
| Sylow | C13 ⋊ ΓL(1,𝔽8)×C29 |
| Sylow | C7 ⋊ C29×C13⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C29 | #63270 |
| commutator, hypocenter | C7×C13 | C3×C29 |
| Frattini | C1 | G |
| Fitting, socle | C7×C13×C29 | C3 |
| LCS | G ▷ C7×C13 | |
| UCS | C1 ◁ C29 | |
16 conjugacy classes of subgroups.
957 conjugacy classes — view the full character table.
| maximal subgroup of | C2×C29×#63270, D29×#63270, C29×#10587716, … |
| maximal normal subgroup of | C2×C29×#63270, D29×#63270, C29×#10587716, … |
| maximal quotient of | C2×C29×#63270, C29×#11717941, C3×C29×#63270, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7917, 5);