Finite Group DatabasebetaFinite Group Databasebeta| order | 972 |
| isoclinism | isoclinic class of #92297 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C32 |
No aliases for this group.
| derived | C32×C9 ⋊ C3×C4 |
| Sylow | C9×H(3,𝔽3) ⋊ C4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | #92297 |
| commutator, hypocenter | C32×C9 | C3×C4 |
| Frattini, socle | C2×C32 | C3×C3⋊D3 |
| Fitting | C2×C9×H(3,𝔽3) | C2 |
| prime radical | C2×C3×H(3,𝔽3) | D3 |
| cosocle | C2×C32×C9 | C2×C3 |
| LCS | G ▷ C32×C9 | |
| UCS | C1 ◁ C2 | |
191 conjugacy classes of subgroups; only the 56 normal subgroups are shown.
This group has 191 conjugacy classes of subgroups — too many to draw. Only its 56 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 324 |
Polycyclic presentation:
2,3,2,3^4|a^2=c,d^3=g,d^a=d^2g^2,e^a=e^2,f^a=f^2,g^a=g^2,e^b=ef108 conjugacy classes — view the full character table.
| maximal subgroup of | Dic9×(C3⋊D3)⋊C3, D9×(C3⋊Dic3)⋊C3, #14516779, … |
| maximal normal subgroup of | Dic9×(C3⋊D3)⋊C3, D9×(C3⋊Dic3)⋊C3, #14516779, … |
| maximal quotient of | #14516330, C2×#11757601 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(972, 326);