Finite Group DatabasebetaFinite Group Databasebeta| order | 864 |
| isoclinism | isoclinic class of D27 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C23 |
| direct product | C2×C8×D27 |
| Fitting | C2×C8×C27 ⋊ C2 |
| derived, Sylow | C27 ⋊ C22×C8 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C8 | D27 |
| commutator, hypocenter | C27 | C22×C8 |
| Frattini | C4×C9 | C22×D3 |
| Fitting | C2×C8×C27 | C2 |
| socle | C22×C3 | C4×D9 |
| prime radical | C22×D27 | C4 |
| cosocle | C4×C27 | C23 |
| LCS | G ▷ C27 | |
| UCS | C1 ◁ C2×C8 | |
152 conjugacy classes of subgroups.
| transitive degree | μt(G) = 432 |
240 conjugacy classes — view the full character table.
| maximal subgroup of | (C2×D27)⋊C16, C4×C8×D27, C8×D108, … |
| maximal normal subgroup of | (C2×D27)⋊C16, C4×C8×D27, C8×D108, … |
| maximal quotient of | C8×Dic54, C4×C8×D27, #13134192, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(864, 116);