Finite Group DatabasebetaFinite Group Databasebeta| order | 1148 |
| isoclinism | isoclinic class of #4223 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C7 · Schur multiplier (H2) = C1 |
| direct product | C7×#4223 |
| Fitting, socle, Hall | C7×C41 ⋊ C4 |
| derived, Sylow | C41 ⋊ C4×C7 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C7 | #4223 |
| commutator, hypocenter | C41 | C4×C7 |
| Frattini | C1 | G |
| Fitting, socle | C7×C41 | C4 |
| prime radical | C7×D41 | C2 |
| cosocle | D41 | C2×C7 |
| LCS | G ▷ C41 | |
| UCS | C1 ◁ C7 | |
12 conjugacy classes of subgroups.
| transitive degree | μt(G) = 287 |
98 conjugacy classes — view the full character table.
| maximal subgroup of | ΓL(1,𝔽8)×#4223, C3×C7×#4223, C7×C3⋊#4223, … |
| maximal normal subgroup of | ΓL(1,𝔽8)×#4223, C3×C7×#4223, C7×C11×#4223, … |
| maximal quotient of | C3×C7×#4223, C7×C3⋊#4223, C7×C11×#4223, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1148, 5);