Finite Group DatabasebetaFinite Group Databasebeta| order | 12300 |
| automorphism | ? |
| homology | Abelianization (H1) = C5 · Schur multiplier (H2) = C2 |
| direct product | A5×C41⋊C5 |
| unambiguous semidirect product | C41⋊(C5×A5) |
| unambiguous semidirect product | (C41×A5)⋊C5 |
| Fitting, Sylow | C41 ⋊ C5×A5 |
| socle, derived | C41×A5 ⋊ C5 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, socle, hypocenter | C41×A5 | C5 |
| Fitting, cosocle | C41 | C5×A5 |
| LCS | G ▷ C41×A5 | |
| UCS | C1 | |
40 conjugacy classes of subgroups.
65 conjugacy classes — view the full character table.
| maximal subgroup of | C3×A5×C41⋊C5 |
| maximal normal subgroup of | C3×A5×C41⋊C5 |
| maximal quotient of | C3×A5×C41⋊C5 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12300, 198);