Finite Group DatabasebetaFinite Group Databasebeta| order | 5504 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C29 |
| direct product | D4×#10621898 |
| Fitting | C2×C4×D4×C43 ⋊ C2 |
| Sylow | C43 ⋊ D4×#41 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4 | C23×D43 |
| commutator, socle | C22×C43 | C25 |
| Frattini | C22 | C24×D43 |
| Fitting | C2×C4×D4×C43 | C2 |
| hypercenter | C2×C4×D4 | D43 |
| hypocenter | C43 | D4×#41 |
| LCS | G ▷ C22×C43 ▷ C43 | |
| UCS | C1 ◁ C2×C4 ◁ C2×C4×D4 | |
1648 conjugacy classes of subgroups.
890 conjugacy classes — view the full character table.
| maximal subgroup of | #24988617, #24988621, #25063453, … |
| maximal normal subgroup of | #24988617, #24988621, #25063453, … |
| maximal quotient of | C22⋊C4×#10621898, C4⋊C4×#10621898, D4×#13063282, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5504, 17998);