Finite Group DatabasebetaFinite Group Databasebeta| order | 2156 |
| isoclinism | isoclinic class of D49 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C11 · Schur multiplier (H2) = C2 |
| direct product | C2×C11×D49 |
| unambiguous semidirect product | C49⋊(C22×C11) |
| unambiguous semidirect product | (C2×C49)⋊(C2×C11) |
| Fitting | C2×C11×C49 ⋊ C2 |
| derived, Sylow | C49 ⋊ C22×C11 |
| Hall | C11×C49 ⋊ C22 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C11 | D49 |
| commutator, cosocle, hypocenter | C49 | C22×C11 |
| Frattini | C7 | C2×C11×D7 |
| Fitting | C2×C11×C49 | C2 |
| socle | C2×C7×C11 | D7 |
| LCS | G ▷ C49 | |
| UCS | C1 ◁ C2×C11 | |
30 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1078 |
572 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×D49×C121, C11×D11×D49, C2×C11×D539, … |
| maximal normal subgroup of | C2×D49×C121, C2×C112×D49, C2×C11×C13×D49, … |
| maximal quotient of | C2×D49×C121, C11×D11×D49, C2×C11×D539, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2156, 8);