Finite Group DatabasebetaFinite Group Databasebeta| order | 864 |
| isoclinism | isoclinic class of C3⋊#157 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C26×C3 |
| direct product | C23×C3⋊#157 |
| Fitting, socle | C23×C33 ⋊ C4 |
| derived, Sylow | C33 ⋊ C23×C4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C23 | C3⋊#157 |
| commutator, hypocenter | C33 | C23×C4 |
| Frattini | C1 | G |
| Fitting, socle | C23×C33 | C4 |
| prime radical | C23×C3×C3⋊D3 | C2 |
| cosocle | C3×C3⋊D3 | C24 |
| LCS | G ▷ C33 | |
| UCS | C1 ◁ C23 | |
804 conjugacy classes of subgroups.
| transitive degree | μt(G) = 96 |
96 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#11722722, #13166603, #13166610, … |
| maximal normal subgroup of | C2×#11722722, #13166603, #13166610, … |
| maximal quotient of | C22×#88988, C22×#88989, C2×#11724511, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(864, 4716);