Finite Group DatabasebetaFinite Group Databasebeta| order | 1216 |
| isoclinism | isoclinic class of D19 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4 · Schur multiplier (H2) = C210 |
| direct product | C23×C4×D19 |
| Fitting | C23×C4×C19 ⋊ C2 |
| derived, Sylow | C19 ⋊ C24×C4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C23×C4 | D19 |
| commutator, hypocenter | C19 | C24×C4 |
| Frattini | C2 | C24×D19 |
| Fitting | C23×C4×C19 | C2 |
| socle | C24×C19 | C22 |
| prime radical | C24×D19 | C2 |
| cosocle | C2×C19 | C25 |
| LCS | G ▷ C19 | |
| UCS | C1 ◁ C23×C4 | |
1362 conjugacy classes of subgroups.
| transitive degree | μt(G) = 608 |
352 conjugacy classes. The character table is too large to display.
| maximal subgroup of | (C2×D19)⋊#95, #14563544, C2×#95×D19, … |
| maximal normal subgroup of | (C2×D19)⋊#95, #14563544, C2×#95×D19, … |
| maximal quotient of | C22×C42×D19, C23×C4×Dic19, C22×C22⋊C4×D19, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1216, 1367);