Finite Group DatabasebetaFinite Group Databasebeta| order | 10706 |
| automorphism | Aut(G) order 27835600 |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C1 |
| dihedral | D5353 |
| unambiguous semidirect product | C53⋊D101 |
| unambiguous semidirect product | C101⋊D53 |
| Fitting, socle, derived, Hall | C53×C101 ⋊ C2 |
| Sylow | C101 ⋊ D53 |
| Sylow | C53 ⋊ D101 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C53×C101 | C2 |
| LCS | G ▷ C53×C101 | |
| UCS | C1 | |
8 conjugacy classes of subgroups.
Polycyclic presentation:
2,53,101|b^a=b^52,c^a=c^1002678 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #36339126, #36339127, D53×D101, … |
| maximal normal subgroup of | #36339126, #36339127, D53×D101, … |
| maximal quotient of | Dic5353, C2×D5353, C3×D5353, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10706, 3);