Finite Group DatabasebetaFinite Group Databasebeta| order | 648 |
| isoclinism | isoclinic class of C3⋊#1113 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2×C3 |
No aliases for this group.
| derived, Sylow | C34 ⋊ C2×C4 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | C3⋊#1113 |
| commutator, hypocenter | C34 | C2×C4 |
| Fitting, socle, cosocle | C2×C34 | C22 |
| prime radical | C2×C32×C3⋊D3 | C2 |
| LCS | G ▷ C34 | |
| UCS | C1 ◁ C2 | |
374 conjugacy classes of subgroups.
| transitive degree | μt(G) = 72 |
Polycyclic presentation:
2^3,3^4|a^2=c,b^2=c,d^a=d^2,e^a=e^2,g^a=g^2,d^b=d^2,e^b=e^2,f^b=f^266 conjugacy classes — view the full character table.
| maximal subgroup of | D32⋊(C3⋊Dic3), #13049433, #13049443, … |
| maximal normal subgroup of | D32⋊(C3⋊Dic3), #13049433, #13049443, … |
| maximal quotient of | #13049083, #13049085, C3⋊#88813, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(648, 674);