Finite Group DatabasebetaFinite Group Databasebeta| order | 5504 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C32 · Schur multiplier (H2) = C4 |
| direct product | C4×C43⋊C32 |
| derived, Sylow | C43 ⋊ C4×C32 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C4×C16 | D43 |
| commutator, hypocenter | C43 | C4×C32 |
| Frattini | C2×C16 | C2×D43 |
| Fitting | C4×C16×C43 | C2 |
| socle | C22×C43 | C2×C16 |
| LCS | G ▷ C43 | |
| UCS | C1 ◁ C4×C16 | |
72 conjugacy classes of subgroups.
1472 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C32×C43⋊C8, C8×C43⋊C32, #24983924, … |
| maximal normal subgroup of | C32×C43⋊C8, C8×C43⋊C32, #24983924, … |
| maximal quotient of | C8×C43⋊C32, #24983928, #24984284, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5504, 2642);