Finite Group DatabasebetaFinite Group Databasebeta| order | 864 |
| isoclinism | isoclinic class of Dic108 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
| direct product | C2×D216 |
| Fitting | C2×C8×C27 ⋊ C2 |
| Sylow | C27 ⋊ C2×D8 |
| subgroup | G/H | |
|---|---|---|
| center | C22 | D108 |
| commutator, cosocle | C4×C27 | C23 |
| Frattini | C4×C9 | C22×D3 |
| Fitting | C2×C8×C27 | C2 |
| socle | C22×C3 | D36 |
| hypercenter | C2×C8 | D27 |
| hypocenter | C27 | C2×D8 |
| LCS | G ▷ C4×C27 ▷ C2×C27 ▷ C27 | |
| UCS | C1 ◁ C22 ◁ C2×C4 ◁ C2×C8 | |
152 conjugacy classes of subgroups.
| transitive degree | μt(G) = 432 |
222 conjugacy classes — view the full character table.
| maximal subgroup of | #13133988, #13133992, #13134005, … |
| maximal normal subgroup of | #13133988, #13133992, #13134005, … |
| maximal quotient of | #13134187, C4×D216, #13134201, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(864, 120);