Finite Group DatabasebetaFinite Group Databasebeta| order | 1216 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
| unambiguous semidirect product | C19⋊#401 |
| Sylow | C19 ⋊ #401 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C22×D19 |
| commutator, socle, prime radical, cosocle | C23×C19 | C23 |
| Fitting | C19×#95 | C2 |
| hypercenter | #95 | D19 |
| hypocenter | C19 | #401 |
| LCS | G ▷ C23×C19 ▷ C19 | |
| UCS | C1 ◁ C23 ◁ #95 | |
118 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1216 |
Polycyclic presentation:
2^6,19|a^2=def,b^2=de,c^2=d,b^a=bd,c^a=ce,c^b=cf,g^c=g^18202 conjugacy classes — view the full character table.
| maximal subgroup of | D19×#401, C2×C19⋊#401, #14566932, … |
| maximal normal subgroup of | D19×#401, C2×C19⋊#401, #14566932, … |
| maximal quotient of | #14561895, #14561896, #14561897, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1216, 492);