Finite Group DatabasebetaFinite Group Databasebeta| order | 1936 |
| isoclinism | isoclinic class of #92150 |
| automorphism | ? |
| homology | Abelianization (H1) = C16 · Schur multiplier (H2) = C11 |
No aliases for this group.
| derived, Sylow | C112 ⋊ C16 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C4 | #92150 |
| commutator, hypocenter | C112 | C16 |
| Fitting | C4×C112 | C4 |
| socle, prime radical | C2×C112 | C8 |
| cosocle | C11⋊(C11⋊C8) | C2 |
| LCS | G ▷ C112 | |
| UCS | C1 ◁ C4 | |
34 conjugacy classes of subgroups.
| transitive degree | μt(G) = 176 |
Polycyclic presentation:
2^4,11^2|a^2=b,b^2=c,c^2=d,e^a=e^5f^7,f^a=ef^6,e^b=e^10,f^b=f^10136 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1936, 46);