Finite Group DatabasebetaFinite Group Databasebeta| order | 5504 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C27 |
| direct product | C2×#14582770 |
| Fitting | C22×C4⋊C4×C43 ⋊ C2 |
| Sylow | C43 ⋊ C2×#385 |
| subgroup | G/H | |
|---|---|---|
| center | C24 | C22×D43 |
| commutator | C22×C43 | C23×C4 |
| Frattini | C23 | C23×D43 |
| Fitting | C22×C4⋊C4×C43 | C2 |
| socle | C24×C43 | C23 |
| hypercenter | C22×C4⋊C4 | D43 |
| hypocenter | C43 | C2×#385 |
| LCS | G ▷ C22×C43 ▷ C43 | |
| UCS | C1 ◁ C24 ◁ C22×C4⋊C4 | |
1232 conjugacy classes of subgroups.
896 conjugacy classes — view the full character table.
| maximal subgroup of | #24991975, #24991995, C4×#14582770, … |
| maximal normal subgroup of | #24991975, #24991995, C4×#14582770, … |
| maximal quotient of | C2×(C2×D43)⋊#95, C2×#19132826, C2×#19132827, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5504, 6919);