Finite Group DatabasebetaFinite Group Databasebeta| order | 5504 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Sylow | C43 ⋊ #2571 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C23×D43 |
| commutator, socle | C23×C43 | C24 |
| Fitting | C43×#382 | C2 |
| hypercenter | #382 | D43 |
| hypocenter | C43 | #2571 |
| LCS | G ▷ C23×C43 ▷ C43 | |
| UCS | C1 ◁ C23 ◁ #382 | |
380 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,43|a^2=fg,b^2=eg,c^2=ef,d^2=e,b^a=be,c^a=cf,d^a=de,c^b=cg,h^b=h^42626 conjugacy classes — view the full character table.
| maximal subgroup of | #25155562, #25155566, #25155584, … |
| maximal normal subgroup of | #25155562, #25155566, #25155584, … |
| maximal quotient of | #25018878, #25018879, #25019530, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5504, 9750);