Finite Group DatabasebetaFinite Group Databasebeta| order | 11402 |
| automorphism | Aut(G) order 32495700 |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C1 |
| dihedral | D5701 |
| unambiguous semidirect product | C5701⋊C2 |
| Fitting, socle, derived, Sylow | C5701 ⋊ C2 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C5701 | C2 |
| LCS | G ▷ C5701 | |
| UCS | C1 | |
4 conjugacy classes of subgroups.
Polycyclic presentation:
2,5701|b^a=b^57002852 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #37503587, C2×D5701, D5701⋊C3, … |
| maximal normal subgroup of | #37503587, C2×D5701, D5701⋊C3, … |
| maximal quotient of | Dic5701, C2×D5701, C3×D5701, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11402, 1);