Finite Group DatabasebetaFinite Group Databasebeta| order | 864 |
| isoclinism | isoclinic class of ((C3⋊D3)⋊C3)⋊C2 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C8 · Schur multiplier (H2) = C4 |
No aliases for this group.
| derived, Sylow | H(3,𝔽3) ⋊ C4×C8 |
176 conjugacy classes of subgroups; only the 64 normal subgroups are shown.
This group has 176 conjugacy classes of subgroups — too many to draw. Only its 64 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=d,b^2=c,c^2=e,g^a=g^2,h^a=h^2,f^b=f^2,h^b=h^2,g^f=gh88 conjugacy classes — view the full character table.
| maximal subgroup of | #13137333, #13137334, #13137335, … |
| maximal normal subgroup of | #13137333, #13137334, #13137335, … |
| maximal quotient of | #13134960, #13134961, #13135078, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(864, 277);