Finite Group DatabasebetaFinite Group Databasebeta| order | 12300 |
| isoclinism | isoclinic class of #1043⋊C3 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4×C41 · Schur multiplier (H2) = C1 |
| direct product | C41×#1043⋊C3 |
| unambiguous semidirect product | #1043⋊(C3×C41) |
| unambiguous semidirect product | (C41×#1043)⋊C3 |
| Fitting, socle, Hall | C52×C41 ⋊ C3×C4 |
| derived, Sylow | C52 ⋊ C3×C4×C41 |
| Hall | C41×#1043 ⋊ C3 |
| Hall | C41×C52⋊C3 ⋊ C4 |
| Hall | #1043 ⋊ C3×C41 |
| Hall | C52⋊C3 ⋊ C4×C41 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C41 | #1043⋊C3 |
| commutator, hypocenter | C52 | C3×C4×C41 |
| Frattini | C1 | G |
| Fitting, socle | C52×C41 | C3×C4 |
| prime radical | C41×(C5⋊D5)⋊C3 | C2 |
| cosocle | C5⋊D5 | C2×C3×C41 |
| LCS | G ▷ C52 | |
| UCS | C1 ◁ C41 | |
36 conjugacy classes of subgroups.
574 conjugacy classes — view the full character table.
| maximal subgroup of | C3×C41×#1043⋊C3, C41×C3⋊(#1043⋊C3) |
| maximal normal subgroup of | C3×C41×#1043⋊C3 |
| maximal quotient of | C41×#1043⋊C9, C3×C41×#1043⋊C3, C41×C3⋊(#1043⋊C3) |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12300, 101);