Finite Group DatabasebetaFinite Group Databasebeta| order | 972 |
| isoclinism | isoclinic class of ((C3⋊D3)⋊C27)⋊C2 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | ((C3⋊D3)⋊C27)⋊C2 |
| unambiguous semidirect product | #92172⋊C2 |
| unambiguous semidirect product | #92206⋊C2 |
| Fitting, derived, Sylow | C32⋊C27 ⋊ C22 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, cosocle, hypocenter | C32⋊C27 | C22 |
| Frattini | C3×C9 | D32 |
| socle | C32 | D3×D9 |
| LCS | G ▷ C32⋊C27 | |
| UCS | C1 | |
95 conjugacy classes of subgroups.
| transitive degree | μt(G) = 54 |
Polycyclic presentation:
2^2,3^5|c^3=e,e^3=g,d^a=d^2,f^a=f^2,c^b=c^2e^2g^2,e^b=e^2g^2,f^b=f^2,g^b=g^2,d^c=df51 conjugacy classes — view the full character table.
| maximal subgroup of | C2×((C3⋊D3)⋊C27)⋊C2, #72221850 |
| maximal normal subgroup of | C2×((C3⋊D3)⋊C27)⋊C2, #72221850 |
| maximal quotient of | #14515763, #92206⋊C4, #92172⋊C4, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(972, 107);