Finite Group DatabasebetaFinite Group Databasebeta| order | 864 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
| direct product | C2×#88403 |
| Fitting | C2×Q8×C27 ⋊ C2 |
| Sylow | C27 ⋊ C2×#41 |
| subgroup | G/H | |
|---|---|---|
| center | C22 | C22×D27 |
| commutator, cosocle | C2×C27 | C24 |
| Frattini | C2×C9 | C23×D3 |
| Fitting | C2×Q8×C27 | C2 |
| socle | C22×C3 | C22×D9 |
| hypercenter | C2×Q8 | D27 |
| hypocenter | C27 | C2×#41 |
| LCS | G ▷ C2×C27 ▷ C27 | |
| UCS | C1 ◁ C22 ◁ C2×Q8 | |
328 conjugacy classes of subgroups.
| transitive degree | μt(G) = 432 |
150 conjugacy classes — view the full character table.
| maximal subgroup of | #13134256, #13134309, #13134310, … |
| maximal normal subgroup of | #13134256, #13134309, #13134310, … |
| maximal quotient of | C2×#11720139, C2×#11720141, C2×#11720142, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(864, 639);