Finite Group DatabasebetaFinite Group Databasebeta| order | 7852 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C13 · Schur multiplier (H2) = C1 |
| direct product | C13×Dic151 |
| unambiguous semidirect product | C151⋊(C4×C13) |
| derived, Sylow | C151 ⋊ C4×C13 |
| Hall | C13×C151 ⋊ C4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C13 | D151 |
| commutator, hypocenter | C151 | C4×C13 |
| Frattini | C2 | C13×D151 |
| Fitting, socle | C2×C13×C151 | C2 |
| LCS | G ▷ C151 | |
| UCS | C1 ◁ C2×C13 | |
12 conjugacy classes of subgroups.
2002 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C3×C13×Dic151, C13×Dic453, C13×(C151⋊C3)⋊C4, … |
| maximal normal subgroup of | C3×C13×Dic151, C13×(C151⋊C3)⋊C4, C13⋊C3×Dic151, … |
| maximal quotient of | C3×C13×Dic151, C13×Dic453 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7852, 3);