Finite Group DatabasebetaFinite Group Databasebeta| order | 7056 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C3 · Schur multiplier (H2) = C23 |
| direct product | D4×C3⋊#64424 |
| Fitting | C3×C72×D4 ⋊ C2×C3 |
| Hall | C3×#3861 ⋊ C2×D4 |
| Sylow | C72 ⋊ C3×D3×D4 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2 | C22×C3⋊#64424 |
| commutator, socle, cosocle | C2×C3×C72 | C23×C3 |
| Fitting | C3×C72×D4 | C2×C3 |
| hypercenter | D4 | C3⋊#64424 |
| hypocenter | C3×C72 | C2×C3×D4 |
| LCS | G ▷ C2×C3×C72 ▷ C3×C72 | |
| UCS | C1 ◁ C2 ◁ D4 | |
1160 conjugacy classes of subgroups; only the 158 normal subgroups are shown.
This group has 1160 conjugacy classes of subgroups — too many to draw. Only its 158 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 588 |
165 conjugacy classes — view the full character table.
| maximal subgroup of | D3×D4×#64424, C2×D4×C3⋊#64424 |
| maximal normal subgroup of | D3×D4×#64424, C2×D4×C3⋊#64424 |
| maximal quotient of | C2×D4×C3⋊#64424 |
Past the SmallGroups library coverage — no SmallGroups id.