Finite Group DatabasebetaFinite Group Databasebeta| order | 19058 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C733 · Schur multiplier (H2) = C1 |
| direct product | D13×C733 |
| unambiguous semidirect product | C13⋊(C2×C733) |
| Fitting, socle, Hall | C13×C733 ⋊ C2 |
| derived, Sylow | C13 ⋊ C2×C733 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C733 | D13 |
| commutator, cosocle, hypocenter | C13 | C2×C733 |
| Frattini | C1 | G |
| Fitting, socle | C13×C733 | C2 |
| LCS | G ▷ C13 | |
| UCS | C1 ◁ C733 | |
8 conjugacy classes of subgroups.
| transitive degree | μt(G) = 9529 |
5864 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #261×C733, #49185606, D13×D733, … |
| maximal normal subgroup of | #261×C733, #49185606, D13×D733, … |
| maximal quotient of | Dic13×C733, C2×D13×C733 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(19058, 1);