Finite Group DatabasebetaFinite Group Databasebeta| order | 1216 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Sylow | C19 ⋊ #541 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C23×D19 |
| commutator, socle, cosocle | C22×C19 | C24 |
| Fitting | C19×#117 | C2 |
| prime radical | C23×C19 | C23 |
| hypercenter | #117 | D19 |
| hypocenter | C19 | #541 |
| LCS | G ▷ C22×C19 ▷ C19 | |
| UCS | C1 ◁ C22 ◁ #117 | |
192 conjugacy classes of subgroups.
| transitive degree | μt(G) = 608 |
Polycyclic presentation:
2^6,19|a^2=e,b^2=f,d^2=e,b^a=be,c^a=cf,d^a=de,g^a=g^18,c^b=ce202 conjugacy classes — view the full character table.
| maximal subgroup of | #14573849, #14573851, #14573887, … |
| maximal normal subgroup of | #14573849, #14573851, #14573887, … |
| maximal quotient of | #14566244, #14566287, #14566317, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1216, 1161);