Finite Group DatabasebetaFinite Group Databasebeta| order | 1208 |
| isoclinism | isoclinic class of D151 |
| automorphism | ? |
| homology | Abelianization (H1) = C8 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C151⋊C8 |
| derived, Sylow | C151 ⋊ C8 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C4 | D151 |
| commutator, hypocenter | C151 | C8 |
| Fitting, cosocle | C4×C151 | C2 |
| socle, prime radical | C2×C151 | C4 |
| LCS | G ▷ C151 | |
| UCS | C1 ◁ C4 | |
8 conjugacy classes of subgroups.
| minimal degree | μ(G) = 159 |
| transitive degree | μt(G) = 1208 |
Polycyclic presentation:
2^3,151|a^2=b,b^2=c,d^a=d^150308 conjugacy classes — view the full character table.
| maximal subgroup of | C8×D151, C2×C151⋊C8, #14558987, … |
| maximal normal subgroup of | C8×D151, C2×C151⋊C8, #14558987, … |
| maximal quotient of | C151⋊C16, C2×C151⋊C8 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1208, 6);