Finite Group DatabasebetaFinite Group Databasebeta| order | 864 |
| isoclinism | isoclinic class of #272 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C26 |
| direct product | C23×#1084 |
| derived, Sylow | H(3,𝔽3) ⋊ C23×C4 |
| subgroup | G/H | |
|---|---|---|
| center, socle, hypercenter | C24×C3 | C3⋊D3 |
| commutator, hypocenter | H(3,𝔽3) | C23×C4 |
| Frattini | C2×C3 | C23×C3⋊D3 |
| Fitting, prime radical | C24×H(3,𝔽3) | C2 |
| cosocle | C2×H(3,𝔽3) | C24 |
| LCS | G ▷ H(3,𝔽3) | |
| UCS | C1 ◁ C24×C3 | |
1298 conjugacy classes of subgroups.
| transitive degree | μt(G) = 288 |
160 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#11720334, #13141148, #13141152, … |
| maximal normal subgroup of | C2×#11720334, #13141148, #13141152, … |
| maximal quotient of | C23×#6180, C22×#88538, C22×C4×#1084, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(864, 2646);