Finite Group DatabasebetaFinite Group Databasebeta| order | 11654 |
| automorphism | Aut(G) order 33948102 |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C1 |
| dihedral | D5827 |
| unambiguous semidirect product | C5827⋊C2 |
| Fitting, socle, derived, Sylow | C5827 ⋊ C2 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C5827 | C2 |
| LCS | G ▷ C5827 | |
| UCS | C1 | |
4 conjugacy classes of subgroups.
Polycyclic presentation:
2,5827|b^a=b^58262915 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×D5827, D5827⋊C3, C3×D5827, … |
| maximal normal subgroup of | C2×D5827, D5827⋊C3, C3×D5827 |
| maximal quotient of | Dic5827, C2×D5827, C3×D5827, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11654, 1);