Finite Group DatabasebetaFinite Group Databasebeta| order | 2592 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C26 |
| direct product | C2×(#157⋊D3)⋊D3 |
| Fitting, socle | C2×C34 ⋊ C2×D4 |
| Sylow | C34 ⋊ C22×D4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | (#157⋊D3)⋊D3 |
| commutator, cosocle | C32×C3⋊D3 | C24 |
| Frattini | C1 | G |
| Fitting, socle | C2×C34 | C2×D4 |
| hypocenter | C34 | C22×D4 |
| LCS | G ▷ C32×C3⋊D3 ▷ C34 | |
| UCS | C1 ◁ C2 | |
1946 conjugacy classes of subgroups; only the 135 normal subgroups are shown.
This group has 1946 conjugacy classes of subgroups — too many to draw. Only its 135 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
84 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#72213247, #72220706, #72220719, … |
| maximal normal subgroup of | C2×#72213247, #72220706, #72220719, … |
| maximal quotient of | #72220280, #72220706, D3×(#157⋊D3)⋊D3, … |
Past the SmallGroups library coverage — no SmallGroups id.