Finite Group DatabasebetaFinite Group Databasebeta| order | 864 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | H(3,𝔽3) ⋊ #103 |
169 conjugacy classes of subgroups; only the 50 normal subgroups are shown.
This group has 169 conjugacy classes of subgroups — too many to draw. Only its 50 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 288 |
Polycyclic presentation:
2^5,3^3|a^2=e,b^2=c,d^2=e,b^a=bd,d^a=de,g^a=g^2,h^a=h^2,d^b=de,f^b=f^2,h^b=h^2,g^f=gh58 conjugacy classes — view the full character table.
| maximal subgroup of | #13137339, #13137340, #13137341, … |
| maximal normal subgroup of | #13137339, #13137340, #13137341, … |
| maximal quotient of | #13134963, #13134971, #13134972, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(864, 280);