Finite Group DatabasebetaFinite Group Databasebeta| order | 864 |
| isoclinism | isoclinic class of C9⋊S4 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C24×C3 |
| direct product | C22×C9⋊S4 |
| Fitting | C24×C9 ⋊ D3 |
| derived | C9×A4 ⋊ C23 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22 | C9⋊S4 |
| commutator, cosocle, hypocenter | C9×A4 | C23 |
| Frattini | C3 | C22×C3⋊S4 |
| Fitting | C24×C9 | D3 |
| socle | C24×C3 | C3⋊D3 |
| LCS | G ▷ C9×A4 | |
| UCS | C1 ◁ C22 | |
521 conjugacy classes of subgroups; only the 76 normal subgroups are shown.
This group has 521 conjugacy classes of subgroups — too many to draw. Only its 76 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 108 |
84 conjugacy classes — view the full character table.
| maximal subgroup of | #13146258, #13146969, C2×(C9⋊S4)⋊C4, … |
| maximal normal subgroup of | #13146258, #13146969, C2×(C9⋊S4)⋊C4, … |
| maximal quotient of | C2×#11722366, C2×C4×C9⋊S4, C2×C4⋊(C9⋊S4), … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(864, 4013);