Finite Group DatabasebetaFinite Group Databasebeta| order | 5504 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C26 |
| direct product | #456×D43 |
| Fitting | C43×#456 ⋊ C2 |
| Sylow | C43 ⋊ C2×#456 |
| subgroup | G/H | |
|---|---|---|
| center | C2 | #120×D43 |
| commutator | C2×C4×C43 | C24 |
| Frattini | C2×C4 | C23×D43 |
| Fitting | C43×#456 | C2 |
| socle | C2×C43 | C2×#120 |
| hypercenter | #456 | D43 |
| hypocenter | C43 | C2×#456 |
| LCS | G ▷ C2×C4×C43 ▷ C2×C43 ▷ C43 | |
| UCS | C1 ◁ C2 ◁ C2×C4 ◁ #456 | |
708 conjugacy classes of subgroups; only the 135 normal subgroups are shown.
This group has 708 conjugacy classes of subgroups — too many to draw. Only its 135 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×#1405, #25016866, D43×#2203, … |
| maximal normal subgroup of | D43×#1405, #25016866, D43×#2203, … |
| maximal quotient of | D43×#1603, D43×#1609, D43×#1604, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5504, 13849);