Finite Group DatabasebetaFinite Group Databasebeta| order | 864 |
| isoclinism | isoclinic class of Dic108 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
| direct product | C2×Dic108 |
| Sylow | C27 ⋊ C2×Q16 |
120 conjugacy classes of subgroups.
| transitive degree | μt(G) = 864 |
222 conjugacy classes — view the full character table.
| maximal subgroup of | #13133987, #13133991, #13134002, … |
| maximal normal subgroup of | #13133987, #13133991, #13134002, … |
| maximal quotient of | #13134186, #13134187, C4×Dic108, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(864, 115);