Finite Group DatabasebetaFinite Group Databasebeta| order | 1216 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Sylow | C19 ⋊ Q64 |
| subgroup | G/H | |
|---|---|---|
| center | C2 | #10597283 |
| commutator, cosocle | C16×C19 | C22 |
| Frattini | C16 | C2×D19 |
| Fitting | C19×Q32 | C2 |
| socle, prime radical | C2×C19 | D16 |
| hypercenter | Q32 | D19 |
| hypocenter | C19 | Q64 |
| LCS | G ▷ C16×C19 ▷ C8×C19 ▷ C4×C19 ▷ C2×C19 ▷ C19 | |
| UCS | C1 ◁ C2 ◁ C4 ◁ C8 ◁ C16 ◁ Q32 | |
30 conjugacy classes of subgroups.
| minimal degree | μ(G) = 83 |
| transitive degree | μt(G) = 1216 |
Polycyclic presentation:
2^6,19|a^2=f,b^2=f,c^2=de,d^2=ef,e^2=f,b^a=bc,c^a=cd,d^a=de,e^a=ef,c^b=cd,d^b=de,e^b=ef,g^b=g^18118 conjugacy classes — view the full character table.
| maximal subgroup of | D19×Q64, C2×#11926384, #14565942, … |
| maximal normal subgroup of | D19×Q64, C2×#11926384, #14565942, … |
| maximal quotient of | #14561815, #14561816, #14561834, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1216, 389);