Finite Group DatabasebetaFinite Group Databasebeta| order | 1953 |
| isoclinism | isoclinic class of ΓL(1,𝔽8)×C31⋊C3 |
| automorphism | ? |
| homology | Abelianization (H1) = C32 · Schur multiplier (H2) = C3 |
| Fitting, socle, derived, Hall | C7×C31 ⋊ C32 |
| Sylow | C31 ⋊ C3×ΓL(1,𝔽8) |
| Sylow | C7 ⋊ C3×C31⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C7×C31 | C32 |
| LCS | G ▷ C7×C31 | |
| UCS | C1 | |
24 conjugacy classes of subgroups.
| minimal degree | μ(G) = 38 |
| transitive degree | μt(G) = 217 |
65 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1953, 6);