Finite Group DatabasebetaFinite Group Databasebeta| order | 1100 |
| isoclinism | isoclinic class of D11 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C25 · Schur multiplier (H2) = C2 |
| direct product | C2×D11×C25 |
| Fitting | C2×C11×C25 ⋊ C2 |
| derived, Sylow | C11 ⋊ C22×C25 |
| Hall | C11×C25 ⋊ C22 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C25 | D11 |
| commutator, hypocenter | C11 | C22×C25 |
| Frattini | C5 | C2×C5×D11 |
| Fitting | C2×C11×C25 | C2 |
| socle | C2×C5×C11 | C2×C5 |
| prime radical | C2×C5×D11 | C5 |
| cosocle | C5×C11 | C22×C5 |
| LCS | G ▷ C11 | |
| UCS | C1 ◁ C2×C25 | |
30 conjugacy classes of subgroups.
| transitive degree | μt(G) = 550 |
350 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D3×D11×C25, C2×C3×D11×C25, C2×C25×D33, … |
| maximal normal subgroup of | C2×C3×D11×C25, C2×C11×D11×C25, C2×C13×D11×C25, … |
| maximal quotient of | D3×D11×C25, C2×C3×D11×C25, C2×C25×D33, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1100, 12);