Finite Group DatabasebetaFinite Group Databasebeta| order | 8758 |
| automorphism | Aut(G) order 18391800 |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C1 |
| dihedral | D4379 |
| unambiguous semidirect product | C29⋊D151 |
| unambiguous semidirect product | C151⋊D29 |
| Fitting, socle, derived, Hall | C29×C151 ⋊ C2 |
| Sylow | C151 ⋊ D29 |
| Sylow | C29 ⋊ D151 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C29×C151 | C2 |
| LCS | G ▷ C29×C151 | |
| UCS | C1 | |
8 conjugacy classes of subgroups.
Polycyclic presentation:
2,29,151|b^a=b^28,c^a=c^1502191 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D29×D151, C2×D4379, C3×D4379, … |
| maximal normal subgroup of | D29×D151, C2×D4379, C3×D4379, … |
| maximal quotient of | Dic4379, C2×D4379, C3×D4379, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8758, 3);