Finite Group DatabasebetaFinite Group Databasebeta| order | 11614 |
| automorphism | Aut(G) order 33715442 |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C1 |
| dihedral | D5807 |
| unambiguous semidirect product | C5807⋊C2 |
| Fitting, socle, derived, Sylow | C5807 ⋊ C2 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C5807 | C2 |
| LCS | G ▷ C5807 | |
| UCS | C1 | |
4 conjugacy classes of subgroups.
Polycyclic presentation:
2,5807|b^a=b^58062905 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×D5807, C3×D5807, D17421 |
| maximal normal subgroup of | C2×D5807, C3×D5807 |
| maximal quotient of | Dic5807, C2×D5807, C3×D5807, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11614, 1);