Finite Group DatabasebetaFinite Group Databasebeta| order | 5504 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C29×C4 |
| direct product | C22×#13063322 |
| Fitting | C22×C42×C43 ⋊ C2 |
| Sylow | C43 ⋊ C22×#127 |
| subgroup | G/H | |
|---|---|---|
| center | C24 | C22×D43 |
| commutator | C22×C43 | C25 |
| Frattini | C22 | C24×D43 |
| Fitting | C22×C42×C43 | C2 |
| socle | C24×C43 | C23 |
| hypercenter | C22×C42 | D43 |
| hypocenter | C43 | C22×#127 |
| LCS | G ▷ C22×C43 ▷ C43 | |
| UCS | C1 ◁ C24 ◁ C22×C42 | |
3000 conjugacy classes of subgroups.
1400 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #24988080, #25003134, #25003161, … |
| maximal normal subgroup of | #24988080, #25003134, #25003161, … |
| maximal quotient of | C22×#14582769, C22×#14582801, C2×C4×#13063322, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5504, 17782);