Finite Group DatabasebetaFinite Group Databasebeta| order | 972 |
| isoclinism | isoclinic class of #92299 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C3 |
No aliases for this group.
| derived | C92 ⋊ C3×C4 |
| Sylow | C9×3−1+2 ⋊ C4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | #92299 |
| commutator, hypocenter | C92 | C3×C4 |
| Frattini, socle | C2×C32 | C3×C3⋊D3 |
| Fitting | C2×C9×3−1+2 | C2 |
| prime radical | C2×C33 | C3⋊D3 |
| cosocle | C2×C92 | C2×C3 |
| LCS | G ▷ C92 | |
| UCS | C1 ◁ C2 | |
146 conjugacy classes of subgroups.
| transitive degree | μt(G) = 324 |
Polycyclic presentation:
2,3,2,3^4|a^2=c,d^3=f,e^3=g,d^a=d^2f^2,e^a=e^2g^2,f^a=f^2,g^a=g^2,e^b=eg^2108 conjugacy classes — view the full character table.
| maximal subgroup of | D9×3−1+2⋊C4, Dic9×AGL(1,ℤ/9), #14516791, … |
| maximal normal subgroup of | D9×3−1+2⋊C4, Dic9×AGL(1,ℤ/9), #14516791, … |
| maximal quotient of | #14516332, C2×#11757603 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(972, 328);