Finite Group DatabasebetaFinite Group Databasebeta| order | 5504 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24×C4 |
| direct product | #497×D43 |
| Fitting | C43×#497 ⋊ C2 |
| Sylow | C43 ⋊ C2×#497 |
| subgroup | G/H | |
|---|---|---|
| center | C22 | C2×D4×D43 |
| commutator | C2×C4×C43 | C24 |
| Frattini | C2×C4 | C23×D43 |
| Fitting | C43×#497 | C2 |
| socle | C22×C43 | C22×D4 |
| hypercenter | #497 | D43 |
| hypocenter | C43 | C2×#497 |
| LCS | G ▷ C2×C4×C43 ▷ C2×C43 ▷ C43 | |
| UCS | C1 ◁ C22 ◁ C42 ◁ #497 | |
564 conjugacy classes of subgroups; only the 145 normal subgroups are shown.
This group has 564 conjugacy classes of subgroups — too many to draw. Only its 145 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
368 conjugacy classes — view the full character table.
| maximal subgroup of | D43×#1407, D43×#1659, D43×#1661, … |
| maximal normal subgroup of | D43×#1407, D43×#1659, D43×#1661, … |
| maximal quotient of | D43×#1714, D43×#1716, D43×#1718, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5504, 14946);