Finite Group DatabasebetaFinite Group Databasebeta| order | 5504 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
| direct product | M16×D172 |
| Fitting | C4×M16×C43 ⋊ C2 |
| Sylow | C43 ⋊ D4×M16 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2×C4 | C23×D43 |
| commutator, socle | C22×C43 | C23×C4 |
| Fitting | C4×M16×C43 | C2 |
| hypercenter | C4×M16 | D43 |
| hypocenter | C43 | D4×M16 |
| LCS | G ▷ C22×C43 ▷ C43 | |
| UCS | C1 ◁ C2×C4 ◁ C4×M16 | |
544 conjugacy classes of subgroups.
890 conjugacy classes — view the full character table.
| maximal subgroup of | #24990924, #24990928, #24990938, … |
| maximal normal subgroup of | #24990924, #24990928, #24990938, … |
| maximal quotient of | M16×D344, #25068029, M16×#10621873, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5504, 13248);