Finite Group DatabasebetaFinite Group Databasebeta| order | 5504 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Sylow | C43 ⋊ C4×#125 |
| 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 | C4×#125 |
| LCS | G ▷ C22×C43 ▷ C43 | |
| UCS | C1 ◁ C23 ◁ #387 | |
484 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,43|a^2=g,b^2=f,c^2=e,d^2=eg,b^a=be,c^a=cf,h^c=h^42,h^d=h^42644 conjugacy classes — view the full character table.
| maximal subgroup of | C4×#125×D43, C2×#19137152, C4×#14583426, … |
| maximal normal subgroup of | C4×#125×D43, C2×#19137152, C4×#14583426, … |
| maximal quotient of | #25017769, #25017771, #387×Dic43, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5504, 7067);