Finite Group DatabasebetaFinite Group Databasebeta| order | 16775 |
| automorphism | ? |
| homology | Abelianization (H1) = C11×C25 · Schur multiplier (H2) = C1 |
| direct product | C11×C61⋊C25 |
| unambiguous semidirect product | C61⋊(C11×C25) |
| derived, Sylow | C61 ⋊ C11×C25 |
| Hall | C11×C61 ⋊ C25 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C5×C11 | C61⋊C5 |
| commutator, hypocenter | C61 | C11×C25 |
| Frattini | C5 | C11×C61⋊C5 |
| Fitting, socle, prime radical | C5×C11×C61 | C5 |
| cosocle | C5×C61 | C5×C11 |
| LCS | G ▷ C61 | |
| UCS | C1 ◁ C5×C11 | |
12 conjugacy classes of subgroups.
| transitive degree | μt(G) = 16775 |
935 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×C11×C61⋊C25, C11×D61⋊C25, D11×C61⋊C25, … |
| maximal normal subgroup of | C2×C11×C61⋊C25, C11×D61⋊C25, D11×C61⋊C25, … |
| maximal quotient of | C2×C11×C61⋊C25 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(16775, 3);