Finite Group DatabasebetaFinite Group Databasebeta| order | 5504 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C8 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Sylow | C43 ⋊ #2982 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2×C4 | C23×D43 |
| commutator | C2×C43 | C23×C8 |
| Fitting | C2×C4×Q8×C43 | C2 |
| socle | C22×C43 | C23×C4 |
| hypercenter | C2×C4×Q8 | D43 |
| hypocenter | C43 | #2982 |
| LCS | G ▷ C2×C43 ▷ C43 | |
| UCS | C1 ◁ C2×C4 ◁ C2×C4×Q8 | |
396 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,43|a^2=f,b^2=e,c^2=e,f^2=g,b^a=be,d^a=de,h^a=h^42,c^b=ce908 conjugacy classes — view the full character table.
| maximal subgroup of | #24990463, #24990466, #24991245, … |
| maximal normal subgroup of | #24990463, #24990466, #24991245, … |
| maximal quotient of | #25095328, #25095637, #25106008, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5504, 13591);