Finite Group DatabasebetaFinite Group Databasebeta| order | 12100 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C52 · Schur multiplier (H2) = C2×C5 |
| Fitting, socle, Hall | C22×C112 ⋊ C52 |
| derived, Sylow | C112 ⋊ C22×C52 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22 | C11⋊C52 |
| commutator, cosocle, hypocenter | C112 | C22×C52 |
| Frattini | C1 | G |
| Fitting, socle | C22×C112 | C52 |
| LCS | G ▷ C112 | |
| UCS | C1 ◁ C22 | |
180 conjugacy classes of subgroups.
196 conjugacy classes — view the full character table.
| maximal subgroup of | A4×C11⋊C52, C2×D3×C11⋊C52, C22×C3×C11⋊C52, … |
| maximal normal subgroup of | A4×C11⋊C52, C22×C3×C11⋊C52, C22×(C11⋊C5)⋊AGL(1,𝔽11) |
| maximal quotient of | C2×D3×C11⋊C52, C22×C3×C11⋊C52 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12100, 162);