Finite Group DatabasebetaFinite Group Databasebeta| order | 16775 |
| isoclinism | isoclinic class of C61⋊C5 |
| automorphism | ? |
| homology | Abelianization (H1) = C52×C11 · Schur multiplier (H2) = C5 |
| direct product | C5×C11×C61⋊C5 |
| unambiguous semidirect product | C61⋊(C52×C11) |
| unambiguous semidirect product | (C5×C61)⋊(C5×C11) |
| Fitting, socle | C5×C11×C61 ⋊ C5 |
| derived, Sylow | C61 ⋊ C52×C11 |
| Hall | C11×C61 ⋊ C52 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C5×C11 | C61⋊C5 |
| commutator, cosocle, hypocenter | C61 | C52×C11 |
| Frattini | C1 | G |
| Fitting, socle | C5×C11×C61 | C5 |
| LCS | G ▷ C61 | |
| UCS | C1 ◁ C5×C11 | |
32 conjugacy classes of subgroups.
| transitive degree | μt(G) = 3355 |
935 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C5×C11×D61⋊C5, C5×(C61⋊C5)⋊D11, C5×D11×C61⋊C5, … |
| maximal normal subgroup of | C5×C11×D61⋊C5, C5×(C61⋊C5)⋊D11, C5×D11×C61⋊C5, … |
| maximal quotient of | C2×C5×C11×C61⋊C5 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(16775, 15);