Finite Group DatabasebetaFinite Group Databasebeta| order | 2592 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| direct product | C2×GU(3,𝔽2)⋊C2 |
| Fitting | C2×H(3,𝔽3) ⋊ GL(2,𝔽3) |
| derived | GU(3,𝔽2) ⋊ C22 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | GU(3,𝔽2)⋊C2 |
| commutator, cosocle, hypocenter | GU(3,𝔽2) | C22 |
| Frattini | C3 | C2×AGL(2,𝔽3) |
| Fitting | C2×H(3,𝔽3) | GL(2,𝔽3) |
| socle | C2×C3 | AGL(2,𝔽3) |
| LCS | G ▷ GU(3,𝔽2) | |
| UCS | C1 ◁ C2 | |
301 conjugacy classes of subgroups; only the 16 normal subgroups are shown.
This group has 301 conjugacy classes of subgroups — too many to draw. Only its 16 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
36 conjugacy classes — view the full character table.
| maximal subgroup of | #72214644, C2×#72210405 |
Past the SmallGroups library coverage — no SmallGroups id.