Finite Group DatabasebetaFinite Group Databasebeta| order | 10634 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C13 · Schur multiplier (H2) = C1 |
| direct product | C13×D409 |
| unambiguous semidirect product | C409⋊(C2×C13) |
| Fitting, socle, Hall | C13×C409 ⋊ C2 |
| derived, Sylow | C409 ⋊ C2×C13 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C13 | D409 |
| commutator, cosocle, hypocenter | C409 | C2×C13 |
| Frattini | C1 | G |
| Fitting, socle | C13×C409 | C2 |
| LCS | G ▷ C409 | |
| UCS | C1 ◁ C13 | |
8 conjugacy classes of subgroups.
2678 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C13×#13109888, #36318518, D13×D409, … |
| maximal normal subgroup of | C13×#13109888, #36318518, D13×D409, … |
| maximal quotient of | C13×Dic409, C2×C13×D409, C3×C13×D409, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10634, 2);