Finite Group DatabasebetaFinite Group Databasebeta| order | 5504 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Fitting | C82×C43 ⋊ C2 |
| Sylow | C43 ⋊ #1335 |
| subgroup | G/H | |
|---|---|---|
| center | C8 | D344 |
| commutator | C8×C43 | C2×C8 |
| Frattini | C4×C8 | C2×D43 |
| Fitting | C82×C43 | C2 |
| socle | C2×C43 | D4⋊C8 |
| hypercenter | C82 | D43 |
| hypocenter | C43 | #1335 |
| LCS | G ▷ C8×C43 ▷ C4×C43 ▷ C2×C43 ▷ C43 | |
| UCS | C1 ◁ C8 ◁ C2×C8 ◁ C4×C8 ◁ C82 | |
100 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,43|a^2=d,c^2=eg,d^2=f,e^2=g,f^2=g,b^a=bc,c^a=ce,e^a=eg,h^a=h^42,c^b=ce,e^b=eg,h^b=h^421388 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D43×#1335, C2×#19132569, #25006382, … |
| maximal normal subgroup of | D43×#1335, C2×#19132569, #25006382, … |
| maximal quotient of | #24983247, #24983250, #24983265, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5504, 2484);