Finite Group DatabasebetaFinite Group Databasebeta| order | 5504 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C22×C4 |
No aliases for this group.
| Sylow | C43 ⋊ #2829 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C23×D43 |
| commutator, socle | C23×C43 | C24 |
| Fitting | C43×#392 | C2 |
| hypercenter | #392 | D43 |
| hypocenter | C43 | #2829 |
| LCS | G ▷ C23×C43 ▷ C43 | |
| UCS | C1 ◁ C23 ◁ #392 | |
450 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,43|a^2=eg,d^2=e,b^a=be,c^a=cf,h^a=h^42,c^b=cg,d^b=def,d^c=de488 conjugacy classes — view the full character table.
| maximal subgroup of | D43×#2829, C2×#19142727, #25302991, … |
| maximal normal subgroup of | D43×#2829, C2×#19142727, #25302991, … |
| maximal quotient of | #25027259, #25027273, #25027369, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5504, 12642);