Finite Group DatabasebetaFinite Group Databasebeta| order | 5504 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C8 · Schur multiplier (H2) = C25 |
| direct product | C2×#14583317 |
| Fitting | C2×M32×C43 ⋊ C2 |
| Sylow | C43 ⋊ C2×#504 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C8 | C22×D43 |
| commutator | C2×C43 | C23×C8 |
| Frattini | C8 | C23×D43 |
| Fitting | C2×M32×C43 | C2 |
| socle | C22×C43 | C22×C8 |
| hypercenter | C2×M32 | D43 |
| hypocenter | C43 | C2×#504 |
| LCS | G ▷ C2×C43 ▷ C43 | |
| UCS | C1 ◁ C2×C8 ◁ C2×M32 | |
368 conjugacy classes of subgroups; only the 213 normal subgroups are shown.
This group has 368 conjugacy classes of subgroups — too many to draw. Only its 213 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
920 conjugacy classes — view the full character table.
| maximal subgroup of | #25011692, #25011697, #25011699, … |
| maximal normal subgroup of | #25011692, #25011697, #25011699, … |
| maximal quotient of | C2×#19136193, C2×#19136194, C4×#14583317, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5504, 17610);