Finite Group DatabasebetaFinite Group Databasebeta| order | 1216 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C19×#131 ⋊ C2 |
| Sylow | C19 ⋊ #578 |
| subgroup | G/H | |
|---|---|---|
| center | C2 | C22×D76 |
| commutator, cosocle | C4×C19 | C24 |
| Frattini | C4 | C23×D19 |
| Fitting | C19×#131 | C2 |
| socle | C2×C19 | C22×D4 |
| hypercenter | #131 | D19 |
| hypocenter | C19 | #578 |
| LCS | G ▷ C4×C19 ▷ C2×C19 ▷ C19 | |
| UCS | C1 ◁ C2 ◁ #41 ◁ #131 | |
248 conjugacy classes of subgroups.
| transitive degree | μt(G) = 608 |
Polycyclic presentation:
2^6,19|a^2=f,b^2=f,e^2=f,b^a=be,e^a=ef,g^a=g^18,e^b=ef,g^b=g^18,d^c=df202 conjugacy classes — view the full character table.
| maximal subgroup of | #14565597, #14565601, #14565611, … |
| maximal normal subgroup of | #14565597, #14565601, #14565611, … |
| maximal quotient of | #14572169, #14572235, #14572480, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1216, 1366);