Finite Group DatabasebetaFinite Group Databasebeta| order | 1216 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Sylow | C19 ⋊ #568 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C4 | C23×D19 |
| commutator, socle | C2×C19 | C23×C4 |
| Fitting, prime radical | C2×#41×C19 | C2 |
| cosocle | C4×C19 | C24 |
| hypercenter | C2×#41 | D19 |
| hypocenter | C19 | #568 |
| LCS | G ▷ C2×C19 ▷ C19 | |
| UCS | C1 ◁ C4 ◁ C2×#41 | |
258 conjugacy classes of subgroups.
| transitive degree | μt(G) = 304 |
Polycyclic presentation:
2^6,19|a^2=e,e^2=f,d^a=df,g^a=g^18,c^b=cf214 conjugacy classes — view the full character table.
| maximal subgroup of | #14563854, #14563857, #14563873, … |
| maximal normal subgroup of | #14563854, #14563857, #14563873, … |
| maximal quotient of | #14572054, #14572063, #14572080, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1216, 1316);