Finite Group DatabasebetaFinite Group Databasebeta| order | 5504 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Sylow | C43 ⋊ #2365 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C23×D43 |
| commutator | C22×C43 | C23×C4 |
| Fitting | C2×C4×Q8×C43 | C2 |
| socle | C23×C43 | C24 |
| hypercenter | C2×C4×Q8 | D43 |
| hypocenter | C43 | #2365 |
| LCS | G ▷ C22×C43 ▷ C43 | |
| UCS | C1 ◁ C23 ◁ C2×C4×Q8 | |
552 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,43|a^2=g,b^2=g,c^2=f,d^2=e,b^a=be,c^a=cf,d^b=de,h^c=h^42890 conjugacy classes — view the full character table.
| maximal subgroup of | #25118847, #25118849, #25118869, … |
| maximal normal subgroup of | #25118847, #25118849, #25118869, … |
| maximal quotient of | C4⋊C4×Dic43⋊C4, #25018135, #25018138, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5504, 7564);