Finite Group DatabasebetaFinite Group Databasebeta| order | 15582 |
| isoclinism | isoclinic class of ΓL(1,𝔽8)⋊D7 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C53 · Schur multiplier (H2) = C1 |
| direct product | C53×ΓL(1,𝔽8)⋊D7 |
| unambiguous semidirect product | ΓL(1,𝔽8)⋊(D7×C53) |
| Fitting, socle, Hall | C72×C53 ⋊ C2×C3 |
| derived, Sylow | C72 ⋊ C2×C3×C53 |
| Hall | C7×ΓL(1,𝔽8)×C53 ⋊ C2 |
| Hall | C53×C7⋊D7 ⋊ C3 |
| Hall | C7×ΓL(1,𝔽8) ⋊ C2×C53 |
| Hall | C7⋊D7 ⋊ C3×C53 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C53 | ΓL(1,𝔽8)⋊D7 |
| commutator, cosocle, hypocenter | C72 | C2×C3×C53 |
| Frattini | C1 | G |
| Fitting, socle | C72×C53 | C2×C3 |
| LCS | G ▷ C72 | |
| UCS | C1 ◁ C53 | |
40 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1113 |
1166 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15582, 25);