Finite Group DatabasebetaFinite Group Databasebeta| order | 5504 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C24×C4 |
| direct product | #387×D43 |
| Fitting | C43×#387 ⋊ C2 |
| Sylow | C43 ⋊ C2×#387 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C23×D43 |
| commutator | C22×C43 | C23×C4 |
| Fitting | C43×#387 | C2 |
| socle | C23×C43 | C24 |
| hypercenter | #387 | D43 |
| hypocenter | C43 | C2×#387 |
| LCS | G ▷ C22×C43 ▷ C43 | |
| UCS | C1 ◁ C23 ◁ #387 | |
712 conjugacy classes of subgroups.
644 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#387×D43, D43×#2290, D43×#2295, … |
| maximal normal subgroup of | C2×#387×D43, D43×#2290, D43×#2295, … |
| maximal quotient of | D43×#1434, D43×#1436, #25017769, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5504, 6930);