Finite Group DatabasebetaFinite Group Databasebeta| order | 5504 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C24 |
| direct product | C2×C43⋊#338 |
| unambiguous semidirect product | (C2×C43)⋊#338 |
| Sylow | C43 ⋊ C2×#338 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4 | C4×Dic43 |
| commutator | C4×C43 | C2×C42 |
| Frattini | C22×C4 | C22×D43 |
| Fitting | C22×M16×C43 | C2 |
| socle | C22×C43 | #95 |
| hypercenter | C22×M16 | D43 |
| hypocenter | C43 | C2×#338 |
| LCS | G ▷ C4×C43 ▷ C43 | |
| UCS | C1 ◁ C2×C4 ◁ C22×M16 | |
372 conjugacy classes of subgroups.
884 conjugacy classes — view the full character table.
| maximal subgroup of | #24983731, #24983733, #24983737, … |
| maximal normal subgroup of | #24983731, #24983733, #24983737, … |
| maximal quotient of | C2×#19132425, C2×#19132426, #24986015, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5504, 4213);