Finite Group DatabasebetaFinite Group Databasebeta| order | 11936 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C16 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | D373⋊C16 |
| derived, Sylow | C373 ⋊ C2×C16 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C8 | #13093637 |
| commutator, hypocenter | C373 | C2×C16 |
| Frattini | C4 | C2×#13093637 |
| Fitting | C8×C373 | C4 |
| socle | C2×C373 | C2×C8 |
| prime radical | C2×D373 | C8 |
| cosocle | #15688412 | C22 |
| LCS | G ▷ C373 | |
| UCS | C1 ◁ C8 | |
28 conjugacy classes of subgroups.
Polycyclic presentation:
2^5,373|a^2=c,c^2=d,d^2=e,f^a=f^104,f^b=f^372,f^c=f^372776 conjugacy classes — view the full character table.
| maximal subgroup of | C16×#13093637, #37560309, #37560334, … |
| maximal normal subgroup of | C16×#13093637, #37560309, #37560334, … |
| maximal quotient of | #37560308, #37560317, #37560343, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11936, 219);