Finite Group DatabasebetaFinite Group Databasebeta| order | 5504 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4 · Schur multiplier (H2) = C211 |
| direct product | C23×C22⋊Dic43 |
| Sylow | C43 ⋊ C23×C22⋊C4 |
| subgroup | G/H | |
|---|---|---|
| center | C25 | C2×D43 |
| commutator | C2×C43 | C24×C4 |
| Frattini | C22 | C24×D43 |
| Fitting | C26×C43 | C2 |
| socle | C25×C43 | C22 |
| hypercenter | C26 | D43 |
| hypocenter | C43 | C23×C22⋊C4 |
| LCS | G ▷ C2×C43 ▷ C43 | |
| UCS | C1 ◁ C25 ◁ C26 | |
4632 conjugacy classes of subgroups.
1424 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #24984519, #25001858, #25001894, … |
| maximal normal subgroup of | #24984519, #25001858, #25001894, … |
| maximal quotient of | C23×C43⋊#95, C22×C4×C22⋊Dic43, C22×#14582755, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5504, 17668);