Finite Group DatabasebetaFinite Group Databasebeta| order | 7056 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C3 · Schur multiplier (H2) = C26 |
| direct product | C23×C3⋊#64424 |
| Fitting, socle | C23×C3×C72 ⋊ C2×C3 |
| derived | C3×C72 ⋊ C24×C3 |
| Hall | C3×#3861 ⋊ C24 |
| Sylow | C72 ⋊ C23×C3×D3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C23 | C3⋊#64424 |
| commutator, cosocle, hypocenter | C3×C72 | C24×C3 |
| Frattini | C1 | G |
| Fitting, socle | C23×C3×C72 | C2×C3 |
| LCS | G ▷ C3×C72 | |
| UCS | C1 ◁ C23 | |
2840 conjugacy classes of subgroups; only the 454 normal subgroups are shown.
This group has 2840 conjugacy classes of subgroups — too many to draw. Only its 454 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 1176 |
264 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C23×D3×#64424, C2×D4×C3⋊#64424, C2×#72245961, … |
| maximal normal subgroup of | C23×D3×#64424, C2×D4×C3⋊#64424, C2×#72245961, … |
| maximal quotient of | C2×D4×C3⋊#64424 |
Past the SmallGroups library coverage — no SmallGroups id.