Finite Group DatabasebetaFinite Group Databasebeta| order | 864 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | H(3,𝔽3) ⋊ C4⋊Q8 |
374 conjugacy classes of subgroups; only the 92 normal subgroups are shown.
This group has 374 conjugacy classes of subgroups — too many to draw. Only its 92 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=d,c^2=d,c^a=ce,f^a=f^2,g^a=g^2,c^b=cd,g^f=gh82 conjugacy classes — view the full character table.
| maximal subgroup of | #13135216, #13135785, #13136952, … |
| maximal normal subgroup of | #13135216, #13135785, #13136952, … |
| maximal quotient of | #13144346, #13144348, #13144349, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(864, 1828);