Finite Group DatabasebetaFinite Group Databasebeta| order | 16006 |
| isoclinism | isoclinic class of D151 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C53 · Schur multiplier (H2) = C1 |
| direct product | C53×D151 |
| unambiguous semidirect product | C151⋊(C2×C53) |
| Fitting, socle, Hall | C53×C151 ⋊ C2 |
| derived, Sylow | C151 ⋊ C2×C53 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C53 | D151 |
| commutator, cosocle, hypocenter | C151 | C2×C53 |
| Frattini | C1 | G |
| Fitting, socle | C53×C151 | C2 |
| LCS | G ▷ C151 | |
| UCS | C1 ◁ C53 | |
8 conjugacy classes of subgroups.
| transitive degree | μt(G) = 8003 |
4081 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D53×D151, C2×C53×D151 |
| maximal normal subgroup of | D53×D151, C2×C53×D151 |
| maximal quotient of | C53×Dic151, C2×C53×D151 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(16006, 2);