Finite Group DatabasebetaFinite Group Databasebeta| order | 10842 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Fitting, socle, derived, Hall | C13×C139 ⋊ C2×C3 |
| Hall | #19129429 ⋊ C2 |
| Hall | D1807 ⋊ C3 |
| Sylow | C139 ⋊ D13⋊C3 |
| Sylow | C13 ⋊ D139⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C13×C139 | C2×C3 |
| LCS | G ▷ C13×C139 | |
| UCS | C1 | |
16 conjugacy classes of subgroups.
Polycyclic presentation:
2,3,13,139|c^a=c^12,d^a=d^138,c^b=c^3,d^b=d^96307 conjugacy classes — view the full character table.
| maximal subgroup of | #24925704⋊C2, C2×#24925712, (C13⋊C3)⋊(D139⋊C3), … |
| maximal normal subgroup of | #24925704⋊C2, C2×#24925712, (C13⋊C3)⋊(D139⋊C3), … |
| maximal quotient of | #36343621, C2×#24925712, #45654234, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10842, 23);