Finite Group DatabasebetaFinite Group Databasebeta| order | 5504 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Sylow | C43 ⋊ #2370 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C23×D43 |
| commutator | C22×C43 | C23×C4 |
| Fitting | C43×#387 | C2 |
| socle | C23×C43 | C24 |
| hypercenter | #387 | D43 |
| hypocenter | C43 | #2370 |
| LCS | G ▷ C22×C43 ▷ C43 | |
| UCS | C1 ◁ C23 ◁ #387 | |
464 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,43|a^2=g,b^2=fg,c^2=ef,d^2=e,b^a=be,c^a=cf,d^b=de,h^c=h^42,h^d=h^42638 conjugacy classes — view the full character table.
| maximal subgroup of | D43×#2370, C2×#19137688, #25256251, … |
| maximal normal subgroup of | D43×#2370, C2×#19137688, #25256251, … |
| maximal quotient of | #25018040, #25018141, #25018151, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5504, 7603);