Finite Group DatabasebetaFinite Group Databasebeta| order | 864 |
| isoclinism | isoclinic class of #88528 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
| direct product | C2×#88529 |
| Fitting | C2×C8×H(3,𝔽3) ⋊ C2 |
| Sylow | H(3,𝔽3) ⋊ C2×D8 |
418 conjugacy classes of subgroups.
| transitive degree | μt(G) = 144 |
106 conjugacy classes — view the full character table.
| maximal subgroup of | #13135100, #13135101, #13135812, … |
| maximal normal subgroup of | #13135100, #13135101, #13135812, … |
| maximal quotient of | #13143767, C4×#88529, #13143779, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(864, 1745);