Finite Group DatabasebetaFinite Group Databasebeta| order | 864 |
| isoclinism | isoclinic class of #1088 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C26 |
| direct product | C23×#1088 |
| Fitting | C23×H(3,𝔽3) ⋊ C4 |
| derived, Sylow | H(3,𝔽3) ⋊ C23×C4 |
| subgroup | G/H | |
|---|---|---|
| center, socle, hypercenter | C23×C3 | #157 |
| commutator, hypocenter | H(3,𝔽3) | C23×C4 |
| Frattini | C3 | C23×#157 |
| Fitting | C23×H(3,𝔽3) | C4 |
| prime radical | C23×#272 | C2 |
| cosocle | #272 | C24 |
| LCS | G ▷ H(3,𝔽3) | |
| UCS | C1 ◁ C23×C3 | |
622 conjugacy classes of subgroups.
| transitive degree | μt(G) = 144 |
112 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#11720707, #13146702, #13146707, … |
| maximal normal subgroup of | C2×#11720707, #13146702, #13146707, … |
| maximal quotient of | C22×#88626, C22×#88627, C2×#11722445, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(864, 4031);