Finite Group DatabasebetaFinite Group Databasebeta| order | 864 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | M16×H(3,𝔽3) ⋊ C2 |
| Sylow | H(3,𝔽3) ⋊ #131 |
341 conjugacy classes of subgroups; only the 82 normal subgroups are shown.
This group has 341 conjugacy classes of subgroups — too many to draw. Only its 82 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 144 |
Polycyclic presentation:
2^5,3^3|c^2=d,d^2=e,b^a=be,f^a=f^2,g^a=g^2,c^b=ce,g^f=gh100 conjugacy classes — view the full character table.
| maximal subgroup of | #13136921, #13139165, #13139166, … |
| maximal normal subgroup of | #13136921, #13139165, #13139166, … |
| maximal quotient of | #13143804, #13143810, #13143811, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(864, 1753);