Finite Group DatabasebetaFinite Group Databasebeta| order | 5504 |
| isoclinism | isoclinic class of D43 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C43 · Schur multiplier (H2) = C23×C43 |
| direct product | C2×C42×Dic43 |
| unambiguous semidirect product | (C2×C43)⋊C43 |
| derived, Sylow | C43 ⋊ C2×C43 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22×C42 | D43 |
| commutator, hypocenter | C43 | C2×C43 |
| Frattini | C23 | C23×D43 |
| Fitting | C22×C42×C43 | C2 |
| socle | C24×C43 | C23 |
| LCS | G ▷ C43 | |
| UCS | C1 ◁ C22×C42 | |
1272 conjugacy classes of subgroups.
1472 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×#19132427, #24986038, #336×Dic43, … |
| maximal normal subgroup of | C2×#19132427, #24986038, #336×Dic43, … |
| maximal quotient of | C43×Dic43, C2×#95×Dic43, C2×C4×C43⋊#95, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5504, 6832);