Finite Group DatabasebetaFinite Group Databasebeta| order | 16775 |
| automorphism | ? |
| homology | Abelianization (H1) = C52 · Schur multiplier (H2) = C5 |
| direct product | C5×#16809824 |
| Fitting, socle | C5×C11×C61 ⋊ C5 |
| derived, Hall | C11×C61 ⋊ C52 |
| Sylow | C61 ⋊ C5×C11⋊C5 |
| Sylow | C11 ⋊ C5×C61⋊C5 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C5 | #16809824 |
| commutator, cosocle, hypocenter | C11×C61 | C52 |
| Frattini | C1 | G |
| Fitting, socle | C5×C11×C61 | C5 |
| LCS | G ▷ C11×C61 | |
| UCS | C1 ◁ C5 | |
32 conjugacy classes of subgroups.
| transitive degree | μt(G) = 3355 |
695 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C5×#20269526, C5×#20269520, C5×#20269514, … |
| maximal normal subgroup of | C5×#20269526, C5×#20269520, C5×#20269514, … |
| maximal quotient of | C2×C5×#16809824 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(16775, 10);