Finite Group DatabasebetaFinite Group Databasebeta| order | 7056 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C3 · Schur multiplier (H2) = C23 |
| direct product | C2×#72245938 |
| Hall | C3×#3861 ⋊ C2×D4 |
| Sylow | C72 ⋊ C2×C3×#67 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22 | D3×#64424 |
| commutator, cosocle | C2×C3×C72 | C23×C3 |
| Frattini | C2 | C2×D3×#64424 |
| Fitting, socle | C22×C3×C72 | C22×C3 |
| hypocenter | C3×C72 | C2×C3×D4 |
| LCS | G ▷ C2×C3×C72 ▷ C3×C72 | |
| UCS | C1 ◁ C22 | |
1240 conjugacy classes of subgroups; only the 171 normal subgroups are shown.
This group has 1240 conjugacy classes of subgroups — too many to draw. Only its 171 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 1176 |
150 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#67×#64424, C2×D3×#11924217, C2×#72245946 |
| maximal normal subgroup of | C2×#67×#64424, C2×D3×#11924217, C2×#72245946 |
Past the SmallGroups library coverage — no SmallGroups id.