Finite Group DatabasebetaFinite Group Databasebeta| order | 5504 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C211 |
| direct product | C2×#120×D43 |
| Fitting | C2×#120×C43 ⋊ C2 |
| Sylow | C43 ⋊ C22×#120 |
| subgroup | G/H | |
|---|---|---|
| center | C23 | C23×D43 |
| commutator | C22×C43 | C25 |
| Frattini | C22 | C24×D43 |
| Fitting | C2×#120×C43 | C2 |
| socle | C23×C43 | C24 |
| hypercenter | C2×#120 | D43 |
| hypocenter | C43 | C22×#120 |
| LCS | G ▷ C22×C43 ▷ C43 | |
| UCS | C1 ◁ C23 ◁ C2×#120 | |
4544 conjugacy classes of subgroups; only the 661 normal subgroups are shown.
This group has 4544 conjugacy classes of subgroups — too many to draw. Only its 661 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
644 conjugacy classes — view the full character table.
| maximal subgroup of | #25012055, D43×#1889, D43×#1898, … |
| maximal normal subgroup of | #25012055, D43×#1889, D43×#1898, … |
| maximal quotient of | C2×#379×D43, C2×#385×D43, C2×#386×D43, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5504, 17724);