Finite Group DatabasebetaFinite Group Databasebeta| order | 12100 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C5 · Schur multiplier (H2) = C11 |
| direct product | C5×#14559102 |
| Fitting, socle, Hall | C52×C112 ⋊ C4 |
| derived | C5×C112 ⋊ C4×C5 |
| Sylow | C112 ⋊ C5×Dic5 |
| Sylow | C52 ⋊ #92150 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C5 | #14559102 |
| commutator, hypocenter | C5×C112 | C4×C5 |
| Frattini | C1 | G |
| Fitting, socle | C52×C112 | C4 |
| prime radical | C52×C11⋊D11 | C2 |
| cosocle | C5×C11⋊D11 | C2×C5 |
| LCS | G ▷ C5×C112 | |
| UCS | C1 ◁ C5 | |
128 conjugacy classes of subgroups.
790 conjugacy classes — view the full character table.
| maximal subgroup of | #49137548, #49137549, C5×#20300045, … |
| maximal normal subgroup of | C5×#14559102⋊C3, C3×C5×#14559102 |
| maximal quotient of | C3×C5×#14559102, C5×C3⋊#14559102 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12100, 252);