Finite Group DatabasebetaFinite Group Databasebeta| order | 864 |
| isoclinism | isoclinic class of #1020⋊C3 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32 · Schur multiplier (H2) = C2×C3 |
| direct product | C3×#1020⋊C3 |
| unambiguous semidirect product | #1020⋊C32 |
| unambiguous semidirect product | (C3×#1020)⋊C3 |
| Fitting, socle | C24×C3 ⋊ C3×D3 |
| derived | C22⋊A4 ⋊ C2×C32 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | #1020⋊C3 |
| commutator, cosocle, hypocenter | C22⋊A4 | C2×C32 |
| Frattini | C1 | G |
| Fitting, socle | C24×C3 | C3×D3 |
| LCS | G ▷ C22⋊A4 | |
| UCS | C1 ◁ C3 | |
145 conjugacy classes of subgroups.
| transitive degree | μt(G) = 24 |
42 conjugacy classes — view the full character table.
| maximal subgroup of | C3×(#1020⋊C3)⋊C2, (#1020⋊C3)⋊D3, D3×#1020⋊C3, … |
| maximal normal subgroup of | C3×(#1020⋊C3)⋊C2, (#1020⋊C3)⋊D3, D3×#1020⋊C3, … |
| maximal quotient of | C3×#5932⋊C3, C3×#5934⋊C3, C3×#5936⋊C3, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(864, 4676);