Finite Group DatabasebetaFinite Group Databasebeta| order | 864 |
| isoclinism | isoclinic class of #1088 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C8 · Schur multiplier (H2) = C4 |
| direct product | C4×#6188 |
| derived, Sylow | H(3,𝔽3) ⋊ C4×C8 |
126 conjugacy classes of subgroups.
| transitive degree | μt(G) = 288 |
112 conjugacy classes — view the full character table.
| maximal subgroup of | #13136669, #13136670, #13136671, … |
| maximal normal subgroup of | #13136669, #13136670, #13136671, … |
| maximal quotient of | C4×#88410, #13136881, C8×#6188, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(864, 748);