Finite Group DatabasebetaFinite Group Databasebeta| order | 864 |
| isoclinism | isoclinic class of #1088 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C8 · Schur multiplier (H2) = C4 |
| direct product | C8×#1088 |
| Fitting | C8×H(3,𝔽3) ⋊ C4 |
| derived, Sylow | H(3,𝔽3) ⋊ C4×C8 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3×C8 | #157 |
| commutator, hypocenter | H(3,𝔽3) | C4×C8 |
| Frattini | C3×C4 | C2×#157 |
| Fitting | C8×H(3,𝔽3) | C4 |
| socle | C2×C3 | C4×#157 |
| prime radical | C2×#272 | C2×C4 |
| cosocle | C4×#272 | C22 |
| LCS | G ▷ H(3,𝔽3) | |
| UCS | C1 ◁ C3×C8 | |
110 conjugacy classes of subgroups.
| transitive degree | μt(G) = 144 |
112 conjugacy classes — view the full character table.
| maximal subgroup of | #13136655, #13136656, #13136722, … |
| maximal normal subgroup of | #13136655, #13136656, #13136722, … |
| maximal quotient of | C16×#1088, #13136869, C8×#6188, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(864, 739);