Finite Group DatabasebetaFinite Group Databasebeta| order | 10780 |
| automorphism | Aut(G) order 9055200 |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C1 |
| dicyclic | Dic2695 |
| unambiguous semidirect product | C11⋊Dic245 |
| unambiguous semidirect product | C49⋊Dic55 |
| derived, Hall | C5×C11×C49 ⋊ C4 |
| Hall | C11×C49 ⋊ Dic5 |
| Hall | C5×C49 ⋊ Dic11 |
| Hall | C5×C11 ⋊ Dic49 |
| Sylow | C49 ⋊ Dic55 |
| Sylow | C11 ⋊ Dic245 |
| Sylow | C5 ⋊ Dic539 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | D2695 |
| commutator, hypocenter | C5×C11×C49 | C4 |
| Frattini | C2×C7 | D385 |
| Fitting, cosocle | C2×C5×C11×C49 | C2 |
| socle, prime radical | C2×C5×C7×C11 | D7 |
| LCS | G ▷ C5×C11×C49 | |
| UCS | C1 ◁ C2 | |
36 conjugacy classes of subgroups.
Polycyclic presentation:
2,5,7,11,2,7|a^2=e,c^7=f^6,b^a=b^4,c^a=c^6f,d^a=d^10,f^a=f^62698 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C3×Dic2695, Dic8085, C11⋊((C49⋊C3)⋊Dic5), … |
| maximal normal subgroup of | C3×Dic2695, C11⋊((C49⋊C3)⋊Dic5), Dic5390 |
| maximal quotient of | C3×Dic2695, Dic8085, Dic13475 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10780, 12);