Finite Group DatabasebetaFinite Group Databasebeta| order | 11454 |
| isoclinism | isoclinic class of D83 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C23 · Schur multiplier (H2) = C1 |
| direct product | C3×C23×D83 |
| unambiguous semidirect product | C83⋊(C2×C3×C23) |
| Fitting, socle, Hall | C3×C23×C83 ⋊ C2 |
| derived, Sylow | C83 ⋊ C2×C3×C23 |
| Hall | C23×C83 ⋊ C2×C3 |
| Hall | C3×C83 ⋊ C2×C23 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3×C23 | D83 |
| commutator, cosocle, hypocenter | C83 | C2×C3×C23 |
| Frattini | C1 | G |
| Fitting, socle | C3×C23×C83 | C2 |
| LCS | G ▷ C83 | |
| UCS | C1 ◁ C3×C23 | |
16 conjugacy classes of subgroups.
2967 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C3×D23×D83, D3×C23×D83, D69×D83, … |
| maximal normal subgroup of | C3×D23×D83, D3×C23×D83, D69×D83, … |
| maximal quotient of | C3×C23×Dic83, C2×C3×C23×D83, C9×C23×D83, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11454, 2);