Finite Group DatabasebetaFinite Group Databasebeta| order | 906 |
| isoclinism | isoclinic class of D151⋊C3 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | D151⋊C3 |
| unambiguous semidirect product | (C151⋊C3)⋊C2 |
| Fitting, socle, derived, Sylow | C151 ⋊ C2×C3 |
| Hall | C151⋊C3 ⋊ C2 |
| Hall | D151 ⋊ C3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C151 | C2×C3 |
| LCS | G ▷ C151 | |
| UCS | C1 | |
8 conjugacy classes of subgroups.
| transitive degree | μt(G) = 151 |
Polycyclic presentation:
2,3,151|c^a=c^150,c^b=c^3231 conjugacy classes — view the full character table.
| maximal subgroup of | C2×D151⋊C3, C3×D151⋊C3, C3⋊(D151⋊C3), … |
| maximal normal subgroup of | C2×D151⋊C3, C3×D151⋊C3, C5×D151⋊C3, … |
| maximal quotient of | (C151⋊C3)⋊C4, C2×D151⋊C3, D151⋊C9, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(906, 1);