Finite Group DatabasebetaFinite Group Databasebeta| order | 12100 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C5 · Schur multiplier (H2) = C1 |
| direct product | C11⋊C5×Dic55 |
| derived | C5×C112 ⋊ C4×C5 |
| Hall | C5×C11×C11⋊C5 ⋊ C4 |
| Sylow | C112 ⋊ C5×Dic5 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | C11⋊C5×D55 |
| commutator, hypocenter | C5×C112 | C4×C5 |
| Fitting, socle, cosocle | C2×C5×C112 | C2×C5 |
| prime radical | C2×C5×C11×C11⋊C5 | C2 |
| LCS | G ▷ C5×C112 | |
| UCS | C1 ◁ C2 | |
68 conjugacy classes of subgroups.
406 conjugacy classes — view the full character table.
| maximal subgroup of | C3×C11⋊C5×Dic55, C11⋊C5×Dic165 |
| maximal normal subgroup of | C3×C11⋊C5×Dic55 |
| maximal quotient of | C3×C11⋊C5×Dic55, C11⋊C5×Dic165 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12100, 141);