Finite Group DatabasebetaFinite Group Databasebeta| order | 1944 |
| isoclinism | isoclinic class of #14519481 |
| automorphism | ? |
| homology | Abelianization (H1) = C3 · Schur multiplier (H2) = C33 |
No aliases for this group.
| Fitting, socle | C34 ⋊ SL(2,𝔽3) |
| derived | #10620211 ⋊ C3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, cosocle, hypocenter | #10620211 | C3 |
| Fitting, socle | C34 | SL(2,𝔽3) |
| LCS | G ▷ #10620211 | |
| UCS | C1 | |
179 conjugacy classes of subgroups.
| transitive degree | μt(G) = 36 |
Polycyclic presentation:
3,2^3,3^4|b^2=d,c^2=d,b^a=bc,c^a=b,e^a=ef^2,g^a=gh^2,c^b=cd,e^b=f,f^b=e^2,g^b=gh^2,h^b=g^2h^2,e^c=ef^2,f^c=e^2f^2,g^c=g^2h^2,h^c=g^2h,e^d=e^2,f^d=f^2,g^d=g^2,h^d=h^221 conjugacy classes — view the full character table.
| derived subgroup of | #72227931 |
| maximal subgroup of | #72209637, #72210292, #72210295, … |
| maximal normal subgroup of | #72210292, #72210295, #72210299, … |
| maximal quotient of | #72209952, #72209955, C2×#14519481, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1944, 3875);