Finite Group DatabasebetaFinite Group Databasebeta| order | 864 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | C2×D4×H(3,𝔽3) ⋊ C2 |
| Sylow | H(3,𝔽3) ⋊ #121 |
517 conjugacy classes of subgroups; only the 90 normal subgroups are shown.
This group has 517 conjugacy classes of subgroups — too many to draw. Only its 90 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|b^2=e,c^a=cd,f^a=f^2,g^a=g^2,c^b=ce,g^f=gh82 conjugacy classes — view the full character table.
| maximal subgroup of | #13136943, #13140571, #13140572, … |
| maximal normal subgroup of | #13136943, #13140571, #13140572, … |
| maximal quotient of | #13144291, #13144298, #13144303, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(864, 1815);