Finite Group DatabasebetaFinite Group Databasebeta| order | 1100 |
| isoclinism | isoclinic class of D25 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C11 · Schur multiplier (H2) = C1 |
| direct product | C11×Dic25 |
| derived, Sylow | C25 ⋊ C4×C11 |
| Hall | C11×C25 ⋊ C4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C11 | D25 |
| commutator, hypocenter | C25 | C4×C11 |
| Frattini | C2×C5 | D5×C11 |
| Fitting | C2×C11×C25 | C2 |
| socle, prime radical | C2×C5×C11 | D5 |
| cosocle | C2×C25 | C2×C11 |
| LCS | G ▷ C25 | |
| UCS | C1 ◁ C2×C11 | |
18 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1100 |
308 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C3×C11×Dic25, C11×Dic75, Dic25×C121, … |
| maximal normal subgroup of | C3×C11×Dic25, Dic25×C121, C112×Dic25, … |
| maximal quotient of | C3×C11×Dic25, C11×Dic75, Dic25×C121, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1100, 3);