Finite Group DatabasebetaFinite Group Databasebeta| order | 1216 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C22 |
| direct product | M32×D19 |
| Fitting | C19×M32 ⋊ C2 |
| Sylow | C19 ⋊ C2×M32 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C8 | C22×D19 |
| commutator, socle | C2×C19 | C22×C8 |
| Fitting | C19×M32 | C2 |
| prime radical | C22×D19 | C8 |
| cosocle | C8×C19 | C23 |
| hypercenter | M32 | D19 |
| hypocenter | C19 | C2×M32 |
| LCS | G ▷ C2×C19 ▷ C19 | |
| UCS | C1 ◁ C8 ◁ M32 | |
90 conjugacy classes of subgroups.
| transitive degree | μt(G) = 304 |
220 conjugacy classes — view the full character table.
| maximal subgroup of | D19×#347, #14565238, D19×#349, … |
| maximal normal subgroup of | D19×#347, #14565238, D19×#349, … |
| maximal quotient of | D19×#346, M32×Dic19, #14565228, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1216, 962);