Finite Group DatabasebetaFinite Group Databasebeta| order | 864 |
| isoclinism | isoclinic class of C3⋊#157 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C23×C3 |
| direct product | C22×C3⋊#622 |
| derived, Sylow | C33 ⋊ C22×C8 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C23 | C3⋊#157 |
| commutator, hypocenter | C33 | C22×C8 |
| Frattini | C2 | C22×C3⋊#157 |
| Fitting, socle, prime radical | C23×C33 | C4 |
| cosocle | C3×C3⋊Dic3 | C23 |
| LCS | G ▷ C33 | |
| UCS | C1 ◁ C23 | |
324 conjugacy classes of subgroups.
| transitive degree | μt(G) = 96 |
96 conjugacy classes — view the full character table.
| maximal subgroup of | #13154847, #13155044, #13155175, … |
| maximal normal subgroup of | #13154847, #13155044, #13155175, … |
| maximal quotient of | C22×C3⋊#3708, C2×#11723098, C2×C4×C3⋊#622, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(864, 4486);