Finite Group DatabasebetaFinite Group Databasebeta| order | 864 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C33 ⋊ C2×Q16 |
306 conjugacy classes of subgroups; only the 63 normal subgroups are shown.
This group has 306 conjugacy classes of subgroups — too many to draw. Only its 63 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 96 |
Polycyclic presentation:
2^5,3^3|b^2=e,c^2=de,d^2=e,f^a=f^2,h^a=h^2,c^b=cd,d^b=de,f^b=f^2,g^b=g^284 conjugacy classes — view the full character table.
| maximal subgroup of | #13154942, #13154950, #13155061, … |
| maximal normal subgroup of | #13154942, #13154950, #13155061, … |
| maximal quotient of | #13161639, #13161642, #13161676, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(864, 3616);