Finite Group DatabasebetaFinite Group Databasebeta| order | 1216 |
| isoclinism | isoclinic class of D19 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C8 · Schur multiplier (H2) = C26 |
| direct product | C23×C19⋊C8 |
| derived, Sylow | C19 ⋊ C23×C8 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C23×C4 | D19 |
| commutator, hypocenter | C19 | C23×C8 |
| Frattini | C4 | C23×D19 |
| Fitting | C23×C4×C19 | C2 |
| socle, prime radical | C24×C19 | C4 |
| cosocle | C4×C19 | C24 |
| LCS | G ▷ C19 | |
| UCS | C1 ◁ C23×C4 | |
338 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1216 |
352 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×#11926298, C2×#11926299, #14563332, … |
| maximal normal subgroup of | C2×#11926298, C2×#11926299, #14563332, … |
| maximal quotient of | C22×C4×C19⋊C8, C22×C22⋊(C19⋊C8), C22×C4⋊(C19⋊C8), … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1216, 1306);