Finite Group DatabasebetaFinite Group Databasebeta| order | 5252 |
| isoclinism | isoclinic class of D13 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C101 · Schur multiplier (H2) = C2 |
| direct product | C2×D13×C101 |
| unambiguous semidirect product | C13⋊(C22×C101) |
| unambiguous semidirect product | (C2×C13)⋊(C2×C101) |
| Fitting, socle | C2×C13×C101 ⋊ C2 |
| derived, Sylow | C13 ⋊ C22×C101 |
| Hall | C13×C101 ⋊ C22 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C101 | D13 |
| commutator, hypocenter | C13 | C22×C101 |
| Frattini | C1 | G |
| Fitting, socle | C2×C13×C101 | C2 |
| LCS | G ▷ C13 | |
| UCS | C1 ◁ C2×C101 | |
20 conjugacy classes of subgroups.
1616 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×D13⋊C3×C101, D3×D13×C101, C2×D39×C101, … |
| maximal normal subgroup of | C2×D13⋊C3×C101, C2×C3×D13×C101, C2×D13×C101⋊C5, … |
| maximal quotient of | D3×D13×C101, C2×D39×C101, C2×C3×D13×C101, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5252, 14);