Finite Group DatabasebetaFinite Group Databasebeta| order | 5504 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C29 |
| direct product | C2×#14583540 |
| Fitting | C2×C22⋊Q8×C43 ⋊ C2 |
| Sylow | C43 ⋊ C2×#546 |
| subgroup | G/H | |
|---|---|---|
| center | C23 | C23×D43 |
| commutator | C22×C43 | C25 |
| Frattini | C22 | C24×D43 |
| Fitting | C2×C22⋊Q8×C43 | C2 |
| socle | C23×C43 | C24 |
| hypercenter | C2×C22⋊Q8 | D43 |
| hypocenter | C43 | C2×#546 |
| LCS | G ▷ C22×C43 ▷ C43 | |
| UCS | C1 ◁ C23 ◁ C2×C22⋊Q8 | |
1900 conjugacy classes of subgroups.
638 conjugacy classes — view the full character table.
| maximal subgroup of | #24988287, #25111955, #25112012, … |
| maximal normal subgroup of | #24988287, #25111955, #25112012, … |
| maximal quotient of | C2×#19137415, C2×#19137424, C2×#19137442, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5504, 17956);