Finite Group DatabasebetaFinite Group Databasebeta| order | 8492 |
| automorphism | Aut(G) order 8152320 |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| dihedral | D4246 |
| direct product | C2×D2123 |
| unambiguous semidirect product | (C2×C11)⋊D193 |
| unambiguous semidirect product | (C2×C193)⋊D11 |
| Fitting, socle | C2×C11×C193 ⋊ C2 |
| derived, Hall | C11×C193 ⋊ C22 |
| Sylow | C193 ⋊ C2×D11 |
| Sylow | C11 ⋊ C2×D193 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | D2123 |
| commutator, hypocenter | C11×C193 | C22 |
| Frattini | C1 | G |
| Fitting, socle | C2×C11×C193 | C2 |
| LCS | G ▷ C11×C193 | |
| UCS | C1 ◁ C2 | |
20 conjugacy classes of subgroups.
2126 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×C11⋊(D193⋊C3), D3×D2123, C2×C3×D2123, … |
| maximal normal subgroup of | C2×C11⋊(D193⋊C3), C2×C3×D2123, D8492 |
| maximal quotient of | D3×D2123, C2×C3×D2123, C2×D6369, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8492, 9);