Finite Group DatabasebetaFinite Group Databasebeta| order | 2592 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C33 · Schur multiplier (H2) = C22×C34 |
| direct product | C2×(C22⋊A4)⋊H(3,𝔽3) |
| Fitting | C25×C32 ⋊ C32 |
| Sylow | C25 ⋊ C3×H(3,𝔽3) |
| subgroup | G/H | |
|---|---|---|
| center | C2×C3 | C3×A42 |
| commutator, cosocle | C24×C3 | C2×C33 |
| Frattini | C3 | C2×C3×A42 |
| Fitting | C25×C32 | C32 |
| socle | C25×C3 | C33 |
| hypercenter | C2×C32 | A42 |
| hypocenter | C24 | C2×C3×H(3,𝔽3) |
| LCS | G ▷ C24×C3 ▷ C24 | |
| UCS | C1 ◁ C2×C3 ◁ C2×C32 | |
906 conjugacy classes of subgroups; only the 98 normal subgroups are shown.
This group has 906 conjugacy classes of subgroups — too many to draw. Only its 98 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
128 conjugacy classes — view the full character table.
Past the SmallGroups library coverage — no SmallGroups id.