Finite Group DatabasebetaFinite Group Databasebeta| order | 864 |
| isoclinism | isoclinic class of D27 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C22×C4 |
| direct product | C2×C4×Dic27 |
| unambiguous semidirect product | (C2×C27)⋊C42 |
| derived, Sylow | C27 ⋊ C2×C42 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22×C4 | D27 |
| commutator, hypocenter | C27 | C2×C42 |
| Frattini | C22×C9 | C22×D3 |
| Fitting | C22×C4×C27 | C2 |
| socle, prime radical | C23×C3 | C2×D9 |
| cosocle | C22×C27 | C23 |
| LCS | G ▷ C27 | |
| UCS | C1 ◁ C22×C4 | |
216 conjugacy classes of subgroups.
| transitive degree | μt(G) = 864 |
240 conjugacy classes — view the full character table.
| maximal subgroup of | #13134028, #13134047, #13134054, … |
| maximal normal subgroup of | #13134028, #13134047, #13134054, … |
| maximal quotient of | C2×C4×C27⋊C8, C2×#11720043, C4×#88363, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(864, 138);