Finite Group DatabasebetaFinite Group Databasebeta| order | 10584 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C3 · Schur multiplier (H2) = C23 |
| direct product | D32×#64424 |
| Fitting, socle, derived | C32×C72 ⋊ C23×C3 |
| Hall | C32×#3861 ⋊ C23 |
| Sylow | C72 ⋊ C2×C3×D32 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C32×C72 | C23×C3 |
| LCS | G ▷ C32×C72 | |
| UCS | C1 | |
1620 conjugacy classes of subgroups; only the 146 normal subgroups are shown.
This group has 1620 conjugacy classes of subgroups — too many to draw. Only its 146 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
126 conjugacy classes — view the full character table.
| maximal subgroup of | D32×#64423⋊C2, D32×ΓL(1,𝔽8)⋊AGL(1,𝔽7), D3×C3⋊D3×#64424 |
| maximal normal subgroup of | D32×#64423⋊C2, D32×ΓL(1,𝔽8)⋊AGL(1,𝔽7) |
| maximal quotient of | D3×C3⋊D3×#64424 |
Past the SmallGroups library coverage — no SmallGroups id.