Finite Group DatabasebetaFinite Group Databasebeta| order | 10122 |
| automorphism | Aut(G) order 14575680 |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C1 |
| dihedral | D5061 |
| unambiguous semidirect product | C3⋊D1687 |
| unambiguous semidirect product | C7⋊D723 |
| unambiguous semidirect product | C241⋊D21 |
| Fitting, socle, derived, Hall | C3×C7×C241 ⋊ C2 |
| Hall | C7×C241 ⋊ D3 |
| Hall | C3×C241 ⋊ D7 |
| Sylow | C241 ⋊ D21 |
| Hall | C3×C7 ⋊ D241 |
| Sylow | C7 ⋊ D723 |
| Sylow | C3 ⋊ D1687 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C3×C7×C241 | C2 |
| LCS | G ▷ C3×C7×C241 | |
| UCS | C1 | |
16 conjugacy classes of subgroups.
Polycyclic presentation:
2,3,7,241|b^a=b^2,c^a=c^6,d^a=d^2402532 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D21×D241, D7×D723, D3×D1687, … |
| maximal normal subgroup of | D21×D241, D7×D723, D3×D1687, … |
| maximal quotient of | Dic5061, C2×D5061, D15183, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10122, 12);