Finite Group DatabasebetaFinite Group Databasebeta| order | 5504 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
| direct product | #401×D43 |
| Fitting | C43×#401 ⋊ C2 |
| Sylow | C43 ⋊ C2×#401 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C23×D43 |
| commutator, socle | C23×C43 | C24 |
| Fitting | C43×#401 | C2 |
| hypercenter | #401 | D43 |
| hypocenter | C43 | C2×#401 |
| LCS | G ▷ C23×C43 ▷ C43 | |
| UCS | C1 ◁ C23 ◁ #401 | |
516 conjugacy classes of subgroups.
506 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#401×D43, D43×#2401, D43×#2643, … |
| maximal normal subgroup of | C2×#401×D43, D43×#2401, D43×#2643, … |
| maximal quotient of | D43×#1443, #25018459, #401×Dic43, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5504, 7805);