Finite Group DatabasebetaFinite Group Databasebeta| order | 10226 |
| automorphism | Aut(G) order 26137656 |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C1 |
| dihedral | D5113 |
| unambiguous semidirect product | C5113⋊C2 |
| Fitting, socle, derived, Sylow | C5113 ⋊ C2 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C5113 | C2 |
| LCS | G ▷ C5113 | |
| UCS | C1 | |
4 conjugacy classes of subgroups.
Polycyclic presentation:
2,5113|b^a=b^51122558 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #35205530, C2×D5113, D5113⋊C3, … |
| maximal normal subgroup of | #35205530, C2×D5113, D5113⋊C3, … |
| maximal quotient of | Dic5113, C2×D5113, C3×D5113, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10226, 1);