Finite Group DatabasebetaFinite Group Databasebeta| order | 1216 |
| isoclinism | isoclinic class of D19 |
| automorphism | ? |
| homology | Abelianization (H1) = C26 · Schur multiplier (H2) = C215 |
| direct product | C25×D19 |
| unambiguous semidirect product | C19⋊C26 |
| unambiguous semidirect product | (C2×C19)⋊C25 |
| Fitting, socle | C25×C19 ⋊ C2 |
| derived, Sylow | C19 ⋊ C26 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C25 | D19 |
| commutator, cosocle, hypocenter | C19 | C26 |
| Frattini | C1 | G |
| Fitting, socle | C25×C19 | C2 |
| LCS | G ▷ C19 | |
| UCS | C1 ◁ C25 | |
5650 conjugacy classes of subgroups.
| transitive degree | μt(G) = 608 |
352 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D19×#379, C2×#11926399, #14571911, … |
| maximal normal subgroup of | D19×#379, C2×#11926399, #14571911, … |
| maximal quotient of | C24×C4×D19, C25×Dic19, C23×D4×D19, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1216, 1387);