Finite Group DatabasebetaFinite Group Databasebeta| order | 5504 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C22×C4 |
No aliases for this group.
| Sylow | C43 ⋊ #2653 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C23×D43 |
| commutator, socle | C23×C43 | C24 |
| Fitting | C43×#394 | C2 |
| hypercenter | #394 | D43 |
| hypocenter | C43 | #2653 |
| LCS | G ▷ C23×C43 ▷ C43 | |
| UCS | C1 ◁ C23 ◁ #394 | |
442 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,43|a^2=eg,c^2=e,d^2=f,b^a=be,c^a=cf,c^b=cg,d^c=de,h^c=h^42,h^d=h^42494 conjugacy classes — view the full character table.
| maximal subgroup of | D43×#2653, C2×#19140653, #25263116, … |
| maximal normal subgroup of | D43×#2653, C2×#19140653, #25263116, … |
| maximal quotient of | #25023058, #25023082, #25023175, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5504, 10568);