Finite Group DatabasebetaFinite Group Databasebeta| order | 1216 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C16 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Sylow | C19 ⋊ M64 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C16 | C2×D19 |
| commutator, socle | C2×C19 | C2×C16 |
| Fitting | C2×C16×C19 | C2 |
| prime radical | C22×C19 | C16 |
| cosocle | C16×C19 | C22 |
| hypercenter | C2×C16 | D19 |
| hypocenter | C19 | M64 |
| LCS | G ▷ C2×C19 ▷ C19 | |
| UCS | C1 ◁ C16 ◁ C2×C16 | |
32 conjugacy classes of subgroups.
| transitive degree | μt(G) = 608 |
Polycyclic presentation:
2^6,19|a^2=c,c^2=d,d^2=e,e^2=f,b^a=bf,g^a=g^18328 conjugacy classes — view the full character table.
| maximal subgroup of | #14561770, #14561771, #14561774, … |
| maximal normal subgroup of | #14561770, #14561771, #14561774, … |
| maximal quotient of | #14561769, C22⋊(C19⋊C32), C4⋊(C19⋊C32), … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1216, 383);