Finite Group DatabasebetaFinite Group Databasebeta| order | 5504 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C32 · Schur multiplier (H2) = C23 |
| direct product | C22×C43⋊C32 |
| derived, Sylow | C43 ⋊ C22×C32 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22×C16 | D43 |
| commutator, hypocenter | C43 | C22×C32 |
| Frattini | C16 | C22×D43 |
| Fitting | C22×C16×C43 | C2 |
| socle | C23×C43 | C16 |
| LCS | G ▷ C43 | |
| UCS | C1 ◁ C22×C16 | |
120 conjugacy classes of subgroups.
1472 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #24984283, #24984284, #24984295, … |
| maximal normal subgroup of | #24984283, #24984284, #24984295, … |
| maximal quotient of | C2×C4×C43⋊C32, C2×C22⋊(C43⋊C32), C2×C4⋊(C43⋊C32), … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5504, 6799);