Finite Group DatabasebetaFinite Group Databasebeta| order | 864 |
| isoclinism | isoclinic class of #1088⋊C2 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C26 |
| direct product | C22×#1088⋊C2 |
| unambiguous semidirect product | #1088⋊C23 |
| unambiguous semidirect product | (((C3⋊D3)⋊C3)⋊C2)⋊C23 |
| Fitting | C22×H(3,𝔽3) ⋊ D4 |
| Sylow | H(3,𝔽3) ⋊ C22×D4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22 | #1088⋊C2 |
| commutator, cosocle | #272 | C24 |
| Frattini | C3 | C22×GO+(4,𝔽2) |
| Fitting | C22×H(3,𝔽3) | D4 |
| socle | C22×C3 | GO+(4,𝔽2) |
| hypocenter | H(3,𝔽3) | C22×D4 |
| LCS | G ▷ #272 ▷ H(3,𝔽3) | |
| UCS | C1 ◁ C22 | |
622 conjugacy classes of subgroups; only the 88 normal subgroups are shown.
This group has 622 conjugacy classes of subgroups — too many to draw. Only its 88 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 72 |
52 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(864, 4007);