Finite Group DatabasebetaFinite Group Databasebeta| order | 864 |
| isoclinism | isoclinic class of Dic54 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
| direct product | C2×#88399 |
| Fitting | C22×C4×C27 ⋊ C2 |
| Sylow | C27 ⋊ C2×#41 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4 | C2×D27 |
| commutator, cosocle | C2×C27 | C24 |
| Frattini | C2×C9 | C23×D3 |
| Fitting | C22×C4×C27 | C2 |
| socle | C22×C3 | C22×D9 |
| hypercenter | C22×C4 | D27 |
| hypocenter | C27 | C2×#41 |
| LCS | G ▷ C2×C27 ▷ C27 | |
| UCS | C1 ◁ C2×C4 ◁ C22×C4 | |
328 conjugacy classes of subgroups; only the 127 normal subgroups are shown.
This group has 328 conjugacy classes of subgroups — too many to draw. Only its 127 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 432 |
228 conjugacy classes — view the full character table.
| maximal subgroup of | #13134235, #13134240, #13134241, … |
| maximal normal subgroup of | #13134235, #13134240, #13134241, … |
| maximal quotient of | C2×C4×Dic54, C2×#11720119, #13136208, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(864, 634);