Finite Group DatabasebetaFinite Group Databasebeta| order | 5504 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C29 |
| direct product | #575×D43 |
| Fitting | C43×#575 ⋊ C2 |
| Sylow | C43 ⋊ C2×#575 |
| subgroup | G/H | |
|---|---|---|
| center | C4 | C2×D4×D43 |
| commutator | C4×C43 | C25 |
| Frattini | C4 | C24×D43 |
| Fitting | C43×#575 | C2 |
| socle | C2×C43 | C23×D4 |
| hypercenter | #575 | D43 |
| hypocenter | C43 | C2×#575 |
| LCS | G ▷ C4×C43 ▷ C2×C43 ▷ C43 | |
| UCS | C1 ◁ C4 ◁ C22×C4 ◁ #575 | |
1484 conjugacy classes of subgroups.
506 conjugacy classes — view the full character table.
| maximal subgroup of | D43×#1881, #25098075, D43×#1906, … |
| maximal normal subgroup of | D43×#1881, #25098075, D43×#1906, … |
| maximal quotient of | D43×#2896, D43×#2911, D43×#2943, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5504, 19252);