Finite Group DatabasebetaFinite Group Databasebeta| order | 12100 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C25 · Schur multiplier (H2) = C1 |
| direct product | C4×#15690027 |
| derived, Sylow | C112 ⋊ C4×C25 |
| Hall | C4×C112 ⋊ C25 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C4×C5 | #10597243 |
| commutator, hypocenter | C112 | C4×C25 |
| Frattini | C2×C5 | C2×#10597243 |
| Fitting | C4×C5×C112 | C5 |
| socle, prime radical, cosocle | C2×C5×C112 | C2×C5 |
| LCS | G ▷ C112 | |
| UCS | C1 ◁ C4×C5 | |
126 conjugacy classes of subgroups.
580 conjugacy classes — view the full character table.
| maximal subgroup of | C4×(C112⋊C3)⋊C25, Dic3×#15690027, C3×C4×#15690027 |
| maximal normal subgroup of | C4×(C112⋊C3)⋊C25, C3×C4×#15690027 |
| maximal quotient of | Dic3×#15690027, C3×C4×#15690027 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12100, 65);