Finite Group DatabasebetaFinite Group Databasebeta| order | 1216 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C26 |
No aliases for this group.
| Fitting | C19×#127 ⋊ C2 |
| Sylow | C19 ⋊ D42 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C23×D19 |
| commutator, socle, cosocle | C22×C19 | C24 |
| Fitting | C19×#127 | C2 |
| hypercenter | #127 | D19 |
| hypocenter | C19 | D42 |
| LCS | G ▷ C22×C19 ▷ C19 | |
| UCS | C1 ◁ C22 ◁ #127 | |
428 conjugacy classes of subgroups.
| transitive degree | μt(G) = 304 |
Polycyclic presentation:
2^6,19|b^a=be,c^a=cf,d^b=de,g^b=g^18,g^c=g^18,g^d=g^18151 conjugacy classes — view the full character table.
| maximal subgroup of | #14562687, #14562690, #14562749, … |
| maximal normal subgroup of | #14562687, #14562690, #14562749, … |
| maximal quotient of | #14566456, #14566535, #14566616, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1216, 1184);