Finite Group DatabasebetaFinite Group Databasebeta| order | 12100 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C11 · Schur multiplier (H2) = C1 |
| direct product | C11×C11⋊#1043 |
| unambiguous semidirect product | C11⋊(C11×#1043) |
| Fitting, socle, Hall | C52×C112 ⋊ C4 |
| derived | C52×C11 ⋊ C4×C11 |
| Sylow | C112 ⋊ #1043 |
| Sylow | C52 ⋊ C11×Dic11 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C11 | C11⋊#1043 |
| commutator, hypocenter | C52×C11 | C4×C11 |
| Frattini | C1 | G |
| Fitting, socle | C52×C112 | C4 |
| prime radical | C112×C5⋊D5 | C2 |
| cosocle | C11×C5⋊D5 | C2×C11 |
| LCS | G ▷ C52×C11 | |
| UCS | C1 ◁ C11 | |
176 conjugacy classes of subgroups.
880 conjugacy classes — view the full character table.
| maximal subgroup of | C11×C11⋊(#1043⋊C3), #49137617, C3×C11×C11⋊#1043, … |
| maximal normal subgroup of | C11×C11⋊(#1043⋊C3), C3×C11×C11⋊#1043 |
| maximal quotient of | C3×C11×C11⋊#1043, C11×C3⋊(C11⋊#1043) |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12100, 254);