Finite Group DatabasebetaFinite Group Databasebeta| order | 1100 |
| isoclinism | isoclinic class of D5×D55 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| direct product | D5×D55 |
| unambiguous semidirect product | (C5×D5)⋊D11 |
| unambiguous semidirect product | (D5×C11)⋊D5 |
| Fitting, socle, derived, Hall | C52×C11 ⋊ C22 |
| Sylow | C52 ⋊ C2×D11 |
| Sylow | C11 ⋊ D52 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C52×C11 | C22 |
| LCS | G ▷ C52×C11 | |
| UCS | C1 | |
48 conjugacy classes of subgroups.
| transitive degree | μt(G) = 110 |
116 conjugacy classes — view the full character table.
| maximal subgroup of | #3874⋊D11, C3×D5×D55, D5×D165, … |
| maximal normal subgroup of | C3×D5×D55, D5×C11×D55, D5×C13×D55, … |
| maximal quotient of | C3×D5×D55, D5×D165, D15×D55, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1100, 44);