Finite Group DatabasebetaFinite Group Databasebeta| order | 1936 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Sylow | C112 ⋊ M16 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C4 | D112 |
| commutator, socle | C2×C112 | C2×C4 |
| Fitting, cosocle | C4×C112 | C22 |
| prime radical | C2×C11×D11 | C4 |
| hypocenter | C112 | M16 |
| LCS | G ▷ C2×C112 ▷ C112 | |
| UCS | C1 ◁ C4 | |
60 conjugacy classes of subgroups.
| transitive degree | μt(G) = 176 |
Polycyclic presentation:
2^4,11^2|b^2=c,c^2=d,b^a=bd,f^a=f^10,e^b=e^10190 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1936, 49);