Finite Group DatabasebetaFinite Group Databasebeta| order | 12100 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C52 · Schur multiplier (H2) = C2×C5 |
| direct product | C2×C5×#11925895 |
| Fitting, socle | C2×C5×C112 ⋊ C2×C5 |
| derived, Sylow | C112 ⋊ C22×C52 |
| Hall | C5×#10597243 ⋊ C22 |
| Hall | C2×C11×D11 ⋊ C52 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C5 | #11925895 |
| commutator, cosocle, hypocenter | C112 | C22×C52 |
| Frattini | C1 | G |
| Fitting, socle | C2×C5×C112 | C2×C5 |
| LCS | G ▷ C112 | |
| UCS | C1 ◁ C2×C5 | |
240 conjugacy classes of subgroups.
250 conjugacy classes — view the full character table.
| maximal subgroup of | C2×C5×#10624391⋊C5, C5×D3×#11925895, C2×C3×C5×#11925895, … |
| maximal normal subgroup of | C2×C3×C5×#11925895 |
| maximal quotient of | C5×D3×#11925895, C2×C3×C5×#11925895, C2×C5×C3⋊#11925895 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12100, 216);