Finite Group DatabasebetaFinite Group Databasebeta| order | 5504 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4 · Schur multiplier (H2) = C29 |
| direct product | C2×#131×D43 |
| Fitting | C2×#131×C43 ⋊ C2 |
| Sylow | C43 ⋊ C22×#131 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C8 | C22×D43 |
| commutator | C2×C43 | C24×C4 |
| Frattini | C4 | C24×D43 |
| Fitting | C2×#131×C43 | C2 |
| socle | C22×C43 | C23×C4 |
| hypercenter | C2×#131 | D43 |
| hypocenter | C43 | C22×#131 |
| LCS | G ▷ C2×C43 ▷ C43 | |
| UCS | C1 ◁ C2×C8 ◁ C2×#131 | |
1504 conjugacy classes of subgroups.
920 conjugacy classes — view the full character table.
| maximal subgroup of | #25012040, D43×#1757, D43×#1764, … |
| maximal normal subgroup of | #25012040, D43×#1757, D43×#1764, … |
| maximal quotient of | C2×#405×D43, C4×#131×D43, C2×#131×Dic43, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5504, 19213);