Finite Group DatabasebetaFinite Group Databasebeta| order | 9516 |
| automorphism | Aut(G) order 6851520 |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| dihedral | D4758 |
| direct product | C2×D2379 |
| unambiguous semidirect product | (C2×C3)⋊D793 |
| unambiguous semidirect product | (C2×C13)⋊D183 |
| unambiguous semidirect product | (C2×C61)⋊D39 |
| Fitting, socle | C2×C3×C13×C61 ⋊ C2 |
| derived, Hall | C3×C13×C61 ⋊ C22 |
| Hall | C13×C61 ⋊ C2×D3 |
| Hall | C3×C61 ⋊ C2×D13 |
| Sylow | C61 ⋊ C2×D39 |
| Hall | C3×C13 ⋊ C2×D61 |
| Sylow | C13 ⋊ C2×D183 |
| Sylow | C3 ⋊ C2×D793 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | D2379 |
| commutator, cosocle, hypocenter | C3×C13×C61 | C22 |
| Frattini | C1 | G |
| Fitting, socle | C2×C3×C13×C61 | C2 |
| LCS | G ▷ C3×C13×C61 | |
| UCS | C1 ◁ C2 | |
40 conjugacy classes of subgroups.
2382 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9516, 94);