Finite Group DatabasebetaFinite Group Databasebeta| order | 864 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | Q8×H(3,𝔽3) ⋊ C22 |
| Sylow | H(3,𝔽3) ⋊ H(5,𝔽2) |
621 conjugacy classes of subgroups; only the 114 normal subgroups are shown.
This group has 621 conjugacy classes of subgroups — too many to draw. Only its 114 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 72 |
Polycyclic presentation:
2^5,3^3|c^2=e,d^2=e,d^a=de,g^a=g^2,h^a=h^2,c^b=ce,f^b=f^2,h^b=h^2,d^c=de,g^f=gh52 conjugacy classes — view the full character table.
| maximal subgroup of | #13146650, #13146652, #13149972, … |
| maximal normal subgroup of | #13146650, #13146652, #13149972, … |
| maximal quotient of | #13149387, #13149403, #13149410, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(864, 2488);