Finite Group DatabasebetaFinite Group Databasebeta| order | 5504 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25×C4 |
| direct product | #388×D43 |
| Fitting | C43×#388 ⋊ C2 |
| Sylow | C43 ⋊ C2×#388 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C23×D43 |
| commutator | C22×C43 | C23×C4 |
| Fitting | C43×#388 | C2 |
| socle | C23×C43 | C24 |
| hypercenter | #388 | D43 |
| hypocenter | C43 | C2×#388 |
| LCS | G ▷ C22×C43 ▷ C43 | |
| UCS | C1 ◁ C23 ◁ #388 | |
928 conjugacy classes of subgroups.
644 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#388×D43, D43×#2290, D43×#2293, … |
| maximal normal subgroup of | C2×#388×D43, D43×#2290, D43×#2293, … |
| maximal quotient of | D43×#1434, D43×#1436, D43×#1437, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5504, 6938);