Finite Group DatabasebetaFinite Group Databasebeta| order | 5504 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4 · Schur multiplier (H2) = C29 |
| direct product | C2×C4×#10621900 |
| Fitting | C2×C4×D4×C43 ⋊ C2 |
| Sylow | C43 ⋊ C2×C4×#41 |
| subgroup | G/H | |
|---|---|---|
| center | C22×C4 | C22×D43 |
| commutator | C2×C43 | C24×C4 |
| Frattini | C22 | C24×D43 |
| Fitting | C2×C4×D4×C43 | C2 |
| socle | C23×C43 | C24 |
| hypercenter | C2×C4×D4 | D43 |
| hypocenter | C43 | C2×C4×#41 |
| LCS | G ▷ C2×C43 ▷ C43 | |
| UCS | C1 ◁ C22×C4 ◁ C2×C4×D4 | |
1728 conjugacy classes of subgroups.
920 conjugacy classes — view the full character table.
| maximal subgroup of | #24987970, #25062405, #25062407, … |
| maximal normal subgroup of | #24987970, #25062405, #25062407, … |
| maximal quotient of | C2×C4×#13063281, C2×C4×#13063283, C2×C4×(C22⋊D43)⋊C4, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5504, 17688);