Finite Group DatabasebetaFinite Group Databasebeta| order | 5504 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C29 |
| direct product | #546×D43 |
| Fitting | C43×#546 ⋊ C2 |
| Sylow | C43 ⋊ C2×#546 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C24×D43 |
| commutator, socle | C22×C43 | C25 |
| Fitting | C43×#546 | C2 |
| hypercenter | #546 | D43 |
| hypocenter | C43 | C2×#546 |
| LCS | G ▷ C22×C43 ▷ C43 | |
| UCS | C1 ◁ C22 ◁ #546 | |
1900 conjugacy classes of subgroups.
575 conjugacy classes — view the full character table.
| maximal subgroup of | D43×#3264, D43×#3266, D43×#3267, … |
| maximal normal subgroup of | D43×#3264, D43×#3266, D43×#3267, … |
| maximal quotient of | D4×C22⋊C4×D43, D43×#2339, D43×#2342, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5504, 17951);