Finite Group DatabasebetaFinite Group Databasebeta| order | 1216 |
| isoclinism | isoclinic class of D19 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C8 · Schur multiplier (H2) = C22×C4 |
| direct product | C2×C8×Dic19 |
| derived, Sylow | C19 ⋊ C2×C4×C8 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22×C8 | D19 |
| commutator, hypocenter | C19 | C2×C4×C8 |
| Frattini | C2×C4 | C22×D19 |
| Fitting | C22×C8×C19 | C2 |
| socle, prime radical | C23×C19 | C2×C4 |
| cosocle | C2×C4×C19 | C23 |
| LCS | G ▷ C19 | |
| UCS | C1 ◁ C22×C8 | |
162 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1216 |
352 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #14561712, #14561716, C4×C8×Dic19, … |
| maximal normal subgroup of | #14561712, #14561716, C4×C8×Dic19, … |
| maximal quotient of | C2×C8×C19⋊C8, C2×#11926266, C8×#64520, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1216, 494);