Finite Group DatabasebetaFinite Group Databasebeta| order | 9516 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| direct product | D3×D793 |
| unambiguous semidirect product | (D3×C13)⋊D61 |
| unambiguous semidirect product | (D3×C61)⋊D13 |
| Fitting, socle, derived, Hall | C3×C13×C61 ⋊ C22 |
| Hall | C13×C61 ⋊ C2×D3 |
| Hall | C3×C61 ⋊ C2×D13 |
| Sylow | C61 ⋊ D3×D13 |
| Hall | C3×C13 ⋊ C2×D61 |
| Sylow | C13 ⋊ D3×D61 |
| Sylow | C3 ⋊ C2×D793 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C3×C13×C61 | C22 |
| LCS | G ▷ C3×C13×C61 | |
| UCS | C1 | |
40 conjugacy classes of subgroups.
1194 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D9×D793, D3×#18011732, D3×#18011731, … |
| maximal normal subgroup of | D3×#18011732, D3×#18011731, D3×(C13⋊C3)⋊D61, … |
| maximal quotient of | D9×D793, C3×D3×D793, D3×D2379, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9516, 83);