Finite Group DatabasebetaFinite Group Databasebeta| order | 10718 |
| automorphism | Aut(G) order 27352336 |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C1 |
| dihedral | D5359 |
| unambiguous semidirect product | C23⋊D233 |
| unambiguous semidirect product | C233⋊D23 |
| Fitting, socle, derived, Hall | C23×C233 ⋊ C2 |
| Sylow | C233 ⋊ D23 |
| Sylow | C23 ⋊ D233 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C23×C233 | C2 |
| LCS | G ▷ C23×C233 | |
| UCS | C1 | |
8 conjugacy classes of subgroups.
Polycyclic presentation:
2,23,233|b^a=b^22,c^a=c^2322681 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D23×D233, C2×D5359, C3×D5359, … |
| maximal normal subgroup of | D23×D233, C2×D5359, C3×D5359 |
| maximal quotient of | Dic5359, C2×D5359, C3×D5359, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10718, 3);