Finite Group DatabasebetaFinite Group Databasebeta| order | 864 |
| isoclinism | isoclinic class of #95⋊C3 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C9 · Schur multiplier (H2) = C2×C3 |
| direct product | C9×#95⋊C3 |
| Fitting | C9×#95 ⋊ C3 |
| derived, Sylow | #95 ⋊ C3×C9 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C9 | C42⋊C3 |
| commutator, hypocenter | #95 | C3×C9 |
| Frattini, socle | C23×C3 | C3×A4 |
| Fitting | C9×#95 | C3 |
| prime radical | C3×#95⋊C3 | C3 |
| cosocle | C3×#95 | C32 |
| LCS | G ▷ #95 | |
| UCS | C1 ◁ C2×C9 | |
83 conjugacy classes of subgroups.
| transitive degree | μt(G) = 108 |
108 conjugacy classes — view the full character table.
| derived subgroup of | C9⋊#4621, C9⋊#4622 |
| maximal subgroup of | C9×#4621, C9×#4622, C9⋊#4621, … |
| maximal normal subgroup of | C9×#4621, C9×#4622, C9⋊#4621, … |
| maximal quotient of | C9×#338⋊C3, C2×C9×#95⋊C3 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(864, 303);