Finite Group DatabasebetaFinite Group Databasebeta| order | 12100 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C5 · Schur multiplier (H2) = C2 |
| direct product | C2×C5⋊#11925898 |
| unambiguous semidirect product | (C2×C5)⋊#11925898 |
| Fitting, socle | C2×C5×C112 ⋊ C2×C5 |
| derived | C5×C112 ⋊ C22×C5 |
| Hall | C5×#10597244 ⋊ C22 |
| Sylow | C112 ⋊ C2×C5×D5 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | C5⋊#11925898 |
| commutator, cosocle, hypocenter | C5×C112 | C22×C5 |
| Frattini | C1 | G |
| Fitting, socle | C2×C5×C112 | C2×C5 |
| LCS | G ▷ C5×C112 | |
| UCS | C1 ◁ C2 | |
100 conjugacy classes of subgroups.
166 conjugacy classes — view the full character table.
| maximal subgroup of | D3×C5⋊#11925898, C2×C3×C5⋊#11925898, C2×C3⋊(C5⋊#11925898) |
| maximal normal subgroup of | C2×C3×C5⋊#11925898 |
| maximal quotient of | D3×C5⋊#11925898, C2×C3×C5⋊#11925898, C2×C3⋊(C5⋊#11925898) |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12100, 231);