Finite Group DatabasebetaFinite Group Databasebeta| order | 1936 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Sylow | C112 ⋊ SD16 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | #92150⋊C2 |
| commutator, cosocle | C11⋊Dic11 | C22 |
| Fitting, socle | C2×C112 | D4 |
| prime radical | #11757245 | C2 |
| hypocenter | C112 | SD16 |
| LCS | G ▷ C11⋊Dic11 ▷ C2×C112 ▷ C112 | |
| UCS | C1 ◁ C2 | |
40 conjugacy classes of subgroups.
| transitive degree | μt(G) = 88 |
Polycyclic presentation:
2^4,11^2|b^2=d,c^2=d,b^a=bcd,c^a=cd,e^a=e^10,c^b=cd,e^b=f^10,f^b=e^10,e^c=e^10,f^c=f^1067 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1936, 107);