Finite Group DatabasebetaFinite Group Databasebeta| order | 5504 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C26 |
| direct product | C2×#14582862 |
| Fitting | C22×M16×C43 ⋊ C2 |
| Sylow | C43 ⋊ C2×#407 |
| subgroup | G/H | |
|---|---|---|
| center | C22×C4 | C22×D43 |
| commutator | C22×C43 | C23×C4 |
| Frattini | C2×C4 | C23×D43 |
| Fitting | C22×M16×C43 | C2 |
| socle | C23×C43 | C22×C4 |
| hypercenter | C22×M16 | D43 |
| hypocenter | C43 | C2×#407 |
| LCS | G ▷ C22×C43 ▷ C43 | |
| UCS | C1 ◁ C22×C4 ◁ C22×M16 | |
1008 conjugacy classes of subgroups; only the 285 normal subgroups are shown.
This group has 1008 conjugacy classes of subgroups — too many to draw. Only its 285 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
896 conjugacy classes — view the full character table.
| maximal subgroup of | #25001827, (C2×D43)⋊#338, #25001837, … |
| maximal normal subgroup of | #25001827, (C2×D43)⋊#338, #25001837, … |
| maximal quotient of | C2×#19132921, C2×#19132924, C2×#19132927, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5504, 12945);