Finite Group DatabasebetaFinite Group Databasebeta| order | 8494 |
| automorphism | Aut(G) order 17327760 |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C1 |
| dihedral | D4247 |
| unambiguous semidirect product | C31⋊D137 |
| unambiguous semidirect product | C137⋊D31 |
| Fitting, socle, derived, Hall | C31×C137 ⋊ C2 |
| Sylow | C137 ⋊ D31 |
| Sylow | C31 ⋊ D137 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C31×C137 | C2 |
| LCS | G ▷ C31×C137 | |
| UCS | C1 | |
8 conjugacy classes of subgroups.
Polycyclic presentation:
2,31,137|b^a=b^30,c^a=c^1362125 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D31×D137, C2×D4247, C3×D4247, … |
| maximal normal subgroup of | D31×D137, C2×D4247, C3×D4247, … |
| maximal quotient of | Dic4247, C2×D4247, C3×D4247, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8494, 3);