Finite Group DatabasebetaFinite Group Databasebeta| order | 5504 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C16 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Fitting | C43×M64 ⋊ C2 |
| Sylow | C43 ⋊ #1400 |
| subgroup | G/H | |
|---|---|---|
| center | C8 | (C2×D43)⋊C4 |
| commutator | C22×C43 | C2×C16 |
| Frattini | C2×C16 | C2×D43 |
| Fitting | C43×M64 | C2 |
| socle | C2×C43 | C22⋊C16 |
| hypercenter | M64 | D43 |
| hypocenter | C43 | #1400 |
| LCS | G ▷ C22×C43 ▷ C2×C43 ▷ C43 | |
| UCS | C1 ◁ C8 ◁ C2×C16 ◁ M64 | |
74 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,43|a^2=d,d^2=e,e^2=f,f^2=g,b^a=bc,c^a=cg,d^b=dg,h^b=h^42884 conjugacy classes — view the full character table.
| maximal subgroup of | D43×#1400, C2×#19132734, #25016799, … |
| maximal normal subgroup of | D43×#1400, C2×#19132734, #25016799, … |
| maximal quotient of | #24983935, #24983995, #24984037, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5504, 2649);