Finite Group DatabasebetaFinite Group Databasebeta| order | 12100 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C5 · Schur multiplier (H2) = C2 |
| direct product | D5×(C11⋊C5)⋊D11 |
| unambiguous semidirect product | (D5×C11⋊C5)⋊D11 |
| Fitting, socle, derived | C5×C112 ⋊ C22×C5 |
| Hall | C5×C11×C11⋊C5 ⋊ C22 |
| Sylow | C112 ⋊ C2×C5×D5 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C5×C112 | C22×C5 |
| LCS | G ▷ C5×C112 | |
| UCS | C1 | |
116 conjugacy classes of subgroups.
184 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12100, 205);