Finite Group DatabasebetaFinite Group Databasebeta| order | 864 |
| isoclinism | isoclinic class of #1088 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C23 |
| direct product | C22×#6188 |
| derived, Sylow | H(3,𝔽3) ⋊ C22×C8 |
| subgroup | G/H | |
|---|---|---|
| center, socle, hypercenter | C23×C3 | #157 |
| commutator, hypocenter | H(3,𝔽3) | C22×C8 |
| Frattini | C2×C3 | C22×#157 |
| Fitting, prime radical | C23×H(3,𝔽3) | C4 |
| cosocle | #1084 | C23 |
| LCS | G ▷ H(3,𝔽3) | |
| UCS | C1 ◁ C23×C3 | |
222 conjugacy classes of subgroups.
| transitive degree | μt(G) = 288 |
112 conjugacy classes — view the full character table.
| maximal subgroup of | #13136719, #13136737, #13136941, … |
| maximal normal subgroup of | #13136719, #13136737, #13136941, … |
| maximal quotient of | C22×#88410, C2×#11720779, C2×C4×#6188, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(864, 2420);