Finite Group DatabasebetaFinite Group Databasebeta| order | 1216 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C26 |
No aliases for this group.
| Sylow | C19 ⋊ #379 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C22×D19 |
| commutator | C22×C19 | C22×C4 |
| Fitting, prime radical | C25×C19 | C2 |
| socle, cosocle | C23×C19 | C23 |
| hypercenter | C25 | D19 |
| hypocenter | C19 | #379 |
| LCS | G ▷ C22×C19 ▷ C19 | |
| UCS | C1 ◁ C23 ◁ C25 | |
506 conjugacy classes of subgroups.
| transitive degree | μt(G) = 304 |
Polycyclic presentation:
2^6,19|a^2=f,b^a=bd,c^a=ce,g^a=g^18316 conjugacy classes — view the full character table.
| maximal subgroup of | C19⋊#1304, #14563549, #14563550, … |
| maximal normal subgroup of | C19⋊#1304, #14563549, #14563550, … |
| maximal quotient of | #14561858, #14561876, #14561906, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1216, 405);