Finite Group DatabasebetaFinite Group Databasebeta| order | 16653 |
| isoclinism | isoclinic class of ΓL(1,𝔽8) |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C13×C61 · Schur multiplier (H2) = C1 |
| direct product | C13×ΓL(1,𝔽8)×C61 |
| unambiguous semidirect product | C7⋊(C3×C13×C61) |
| Fitting, socle, Hall | C7×C13×C61 ⋊ C3 |
| derived, Sylow | C7 ⋊ C3×C13×C61 |
| Hall | C7×C61 ⋊ C3×C13 |
| Hall | C7×C13 ⋊ C3×C61 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C13×C61 | ΓL(1,𝔽8) |
| commutator, cosocle, hypocenter | C7 | C3×C13×C61 |
| Frattini | C1 | G |
| Fitting, socle | C7×C13×C61 | C3 |
| LCS | G ▷ C7 | |
| UCS | C1 ◁ C13×C61 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 5551 |
3965 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×C13×ΓL(1,𝔽8)×C61, C13×ΓL(1,𝔽8)×D61, ΓL(1,𝔽8)×D13×C61, … |
| maximal normal subgroup of | C2×C13×ΓL(1,𝔽8)×C61, C13×ΓL(1,𝔽8)×D61, ΓL(1,𝔽8)×D13×C61, … |
| maximal quotient of | C2×C13×ΓL(1,𝔽8)×C61 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(16653, 6);