Finite Group DatabasebetaFinite Group Databasebeta| order | 864 |
| isoclinism | isoclinic class of #272 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C8 · Schur multiplier (H2) = C4 |
| direct product | C4×#6180 |
| derived, Sylow | H(3,𝔽3) ⋊ C4×C8 |
242 conjugacy classes of subgroups.
| transitive degree | μt(G) = 288 |
160 conjugacy classes — view the full character table.
| maximal subgroup of | #13134960, #13134961, #13134962, … |
| maximal normal subgroup of | #13134960, #13134961, #13134962, … |
| maximal quotient of | C8×#6180, #13135747, C4×#88386, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(864, 486);