Finite Group DatabasebetaFinite Group Databasebeta| order | 864 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3×C9 · Schur multiplier (H2) = C2×C3 |
| direct product | C3×#63700 |
| Sylow | H(5,𝔽2) ⋊ C3×C9 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C32 | C22×A4 |
| commutator, hypocenter | Q8 | C22×C3×C9 |
| Frattini | C2×C3 | C22×C3×A4 |
| Fitting, prime radical | C32×H(5,𝔽2) | C3 |
| cosocle | C3×Q8 | C22×C32 |
| hypercenter | C32×Q8 | A4 |
| LCS | G ▷ Q8 | |
| UCS | C1 ◁ C2×C32 ◁ C32×Q8 | |
254 conjugacy classes of subgroups.
| transitive degree | μt(G) = 216 |
171 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(864, 2542);