Finite Group DatabasebetaFinite Group Databasebeta| order | 1216 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C29 |
| direct product | C22×#64545 |
| Fitting | C22×Q8×C19 ⋊ C2 |
| Sylow | C19 ⋊ C22×#41 |
| subgroup | G/H | |
|---|---|---|
| center | C23 | C22×D19 |
| commutator, cosocle | C2×C19 | C25 |
| Frattini | C2 | C24×D19 |
| Fitting | C22×Q8×C19 | C2 |
| socle | C23×C19 | C23 |
| hypercenter | C22×Q8 | D19 |
| hypocenter | C19 | C22×#41 |
| LCS | G ▷ C2×C19 ▷ C19 | |
| UCS | C1 ◁ C23 ◁ C22×Q8 | |
890 conjugacy classes of subgroups.
| transitive degree | μt(G) = 608 |
220 conjugacy classes — view the full character table.
| maximal subgroup of | #14563562, #14563574, #14566124, … |
| maximal normal subgroup of | #14563562, #14563574, #14566124, … |
| maximal quotient of | C22×#10597338, C22×#10597339, C22×Q8×Dic19, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1216, 1377);