Finite Group DatabasebetaFinite Group Databasebeta| order | 864 |
| isoclinism | isoclinic class of D9×C22⋊A4 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C24 |
| direct product | D9×C22⋊A4 |
| Fitting, derived | C24×C9 ⋊ C2×C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, cosocle, hypocenter | C24×C9 | C2×C3 |
| Frattini | C3 | D3×C22⋊A4 |
| socle | C24×C3 | C3×D3 |
| LCS | G ▷ C24×C9 | |
| UCS | C1 | |
458 conjugacy classes of subgroups.
| transitive degree | μt(G) = 108 |
48 conjugacy classes — view the full character table.
| maximal subgroup of | D9×#120⋊C3, D9×#1020, C2×D9×C22⋊A4, … |
| maximal normal subgroup of | D9×#120⋊C3, D9×#1020, C2×D9×C22⋊A4, … |
| maximal quotient of | #13164645, D9×C22⋊SL(2,𝔽3), #13164649, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(864, 4028);