Finite Group DatabasebetaFinite Group Databasebeta| order | 864 |
| isoclinism | isoclinic class of C22⋊A4 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C33 · Schur multiplier (H2) = C24×C33 |
| direct product | C2×C32×C22⋊A4 |
| Fitting, socle | C25×C32 ⋊ C3 |
| derived | C24 ⋊ C2×C33 |
| Sylow | C25 ⋊ C33 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C32 | C22⋊A4 |
| commutator, cosocle, hypocenter | C24 | C2×C33 |
| Frattini | C1 | G |
| Fitting, socle | C25×C32 | C3 |
| LCS | G ▷ C24 | |
| UCS | C1 ◁ C2×C32 | |
1112 conjugacy classes of subgroups.
| transitive degree | μt(G) = 108 |
144 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(864, 4721);