Finite Group DatabasebetaFinite Group Databasebeta| order | 12100 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C5 · Schur multiplier (H2) = C2×C11 |
| direct product | D5×#11925893 |
| Fitting, socle, derived | C5×C112 ⋊ C22×C5 |
| Hall | C5×#10597245 ⋊ 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.
88 conjugacy classes — view the full character table.
| maximal subgroup of | C3×D5×#11925893, D15×#11925893, D5×C3⋊#11925893, … |
| maximal normal subgroup of | C3×D5×#11925893 |
| maximal quotient of | C3×D5×#11925893, D15×#11925893, D5×C3⋊#11925893, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12100, 189);