Finite Group DatabasebetaFinite Group Databasebeta| order | 1936 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Fitting | D4×C121 ⋊ C2 |
| Sylow | C121 ⋊ D8 |
| subgroup | G/H | |
|---|---|---|
| center | C2 | C22⋊D121 |
| commutator, cosocle | C4×C121 | C22 |
| Frattini | C4×C11 | C2×D11 |
| Fitting | D4×C121 | C2 |
| socle | C2×C11 | C22⋊D11 |
| hypercenter | D4 | D121 |
| hypocenter | C121 | D8 |
| LCS | G ▷ C4×C121 ▷ C2×C121 ▷ C121 | |
| UCS | C1 ◁ C2 ◁ C4 ◁ D4 | |
33 conjugacy classes of subgroups.
| minimal degree | μ(G) = 129 |
| transitive degree | μt(G) = 968 |
Polycyclic presentation:
2^4,11^2|c^2=d,e^11=f,b^a=bc,c^a=cd,e^a=e^10f^10,f^a=f^10,c^b=cd307 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1936, 15);