Finite Group DatabasebetaFinite Group Databasebeta| order | 10449 |
| isoclinism | isoclinic class of C43⋊C3 |
| automorphism | ? |
| homology | Abelianization (H1) = C35 · Schur multiplier (H2) = C310 |
| direct product | C34×C43⋊C3 |
| unambiguous semidirect product | C43⋊C35 |
| unambiguous semidirect product | (C3×C43)⋊C34 |
| Fitting, socle | C34×C43 ⋊ C3 |
| derived, Sylow | C43 ⋊ C35 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C34 | C43⋊C3 |
| commutator, cosocle, hypocenter | C43 | C35 |
| Frattini | C1 | G |
| Fitting, socle | C34×C43 | C3 |
| LCS | G ▷ C43 | |
| UCS | C1 ◁ C34 | |
5328 conjugacy classes of subgroups.
1377 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #44532245, C43⋊C3×#6866, C3×#23782711, … |
| maximal normal subgroup of | #44532245, C43⋊C3×#6866, C3×#23782711, … |
| maximal quotient of | C33×C9×C43⋊C3, C34×C43⋊C9, C32×H(3,𝔽3)×C43⋊C3, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10449, 309);