Finite Group DatabasebetaFinite Group Databasebeta| order | 1296 |
| isoclinism | isoclinic class of #10620191 |
| automorphism | ? |
| homology | Abelianization (H1) = C16 · Schur multiplier (H2) = C3 |
No aliases for this group.
| derived, Sylow | C34 ⋊ C16 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | #10620191 |
| commutator, hypocenter | C34 | C16 |
| Fitting, socle, prime radical | C2×C34 | C8 |
| cosocle | C3⋊(C3⋊#622) | C2 |
| LCS | G ▷ C34 | |
| UCS | C1 ◁ C2 | |
98 conjugacy classes of subgroups.
| transitive degree | μt(G) = 48 |
Polycyclic presentation:
2^4,3^4|a^2=b,b^2=c,c^2=d,e^a=e^2f^2,f^a=e^2,g^a=gh,h^a=gh^2,e^b=e^2f,f^b=ef,g^b=g^2,h^b=h^2,e^c=e^2,f^c=f^242 conjugacy classes — view the full character table.
| maximal subgroup of | #72252863, #72252871, #72252873 |
| maximal normal subgroup of | #72252863, #72252871, #72252873 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1296, 3096);