Finite Group DatabasebetaFinite Group Databasebeta| order | 10842 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C1 |
| direct product | C2×#19129428 |
| Fitting, socle, Hall | C2×C13×C139 ⋊ C3 |
| derived, Hall | C13×C139 ⋊ C2×C3 |
| Hall | C2×C139 ⋊ C13⋊C3 |
| Sylow | C139 ⋊ C2×C13⋊C3 |
| Hall | C2×C13 ⋊ C139⋊C3 |
| Sylow | C13 ⋊ C2×C139⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | #19129428 |
| commutator, cosocle, hypocenter | C13×C139 | C2×C3 |
| Frattini | C1 | G |
| Fitting, socle | C2×C13×C139 | C3 |
| LCS | G ▷ C13×C139 | |
| UCS | C1 ◁ C2 | |
16 conjugacy classes of subgroups.
1210 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C4×#19129428, #36343614, #36343618, … |
| maximal normal subgroup of | C4×#19129428, #36343614, #36343618, … |
| maximal quotient of | C4×#19129428, C22×#19129428, C2×#30653617, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10842, 5);