Finite Group DatabasebetaFinite Group Databasebeta| order | 24696 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32×C7 · Schur multiplier (H2) = C2×C3 |
| direct product | A4×#72215772 |
| Fitting | C22×7−1+2 ⋊ C2×C32 |
| derived | C22×C49 ⋊ C2×C32×C7 |
| Hall | C22×D49⋊C7 ⋊ C32 |
| Sylow | 7−1+2 ⋊ C2×C3×A4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, cosocle, hypocenter | C22×C49 | C2×C32×C7 |
| Frattini | C7 | C7×A4×AGL(1,𝔽7) |
| Fitting | C22×7−1+2 | C2×C32 |
| socle | C22×C7 | C3×C7×AGL(1,𝔽7) |
| LCS | G ▷ C22×C49 | |
| UCS | C1 | |
197 conjugacy classes of subgroups; only the 41 normal subgroups are shown.
This group has 197 conjugacy classes of subgroups — too many to draw. Only its 41 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 196 |
200 conjugacy classes — view the full character table.
| maximal subgroup of | S4×#72215772 |
| maximal normal subgroup of | S4×#72215772 |
Past the SmallGroups library coverage — no SmallGroups id.