Finite Group DatabasebetaFinite Group Databasebeta| order | 16775 |
| isoclinism | isoclinic class of C11⋊C5 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C61 · Schur multiplier (H2) = C1 |
| direct product | C61×C11⋊C25 |
| unambiguous semidirect product | C11⋊(C25×C61) |
| derived, Sylow | C11 ⋊ C25×C61 |
| Hall | C11×C61 ⋊ C25 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C5×C61 | C11⋊C5 |
| commutator, hypocenter | C11 | C25×C61 |
| Frattini | C5 | C11⋊C5×C61 |
| Fitting, socle, prime radical | C5×C11×C61 | C5 |
| cosocle | C5×C11 | C5×C61 |
| LCS | G ▷ C11 | |
| UCS | C1 ◁ C5×C61 | |
12 conjugacy classes of subgroups.
| transitive degree | μt(G) = 16775 |
2135 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×C61×C11⋊C25, D61×C11⋊C25, C61×D11⋊C25, … |
| maximal normal subgroup of | C2×C61×C11⋊C25, D61×C11⋊C25, C61×D11⋊C25, … |
| maximal quotient of | C2×C61×C11⋊C25 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(16775, 2);