Finite Group DatabasebetaFinite Group Databasebeta| order | 5504 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Sylow | C43 ⋊ #2396 |
| subgroup | G/H | |
|---|---|---|
| center | C22×C4 | C22×D43 |
| commutator, socle | C23×C43 | C24 |
| Frattini | C23 | C23×D43 |
| Fitting | C2×#117×C43 | C2 |
| hypercenter | C2×#117 | D43 |
| hypocenter | C43 | #2396 |
| LCS | G ▷ C23×C43 ▷ C43 | |
| UCS | C1 ◁ C22×C4 ◁ C2×#117 | |
528 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,43|a^2=f,c^2=f,d^2=e,b^a=be,c^a=cf,c^b=cg,h^c=h^42884 conjugacy classes — view the full character table.
| maximal subgroup of | #24991684, #24991686, #24991689, … |
| maximal normal subgroup of | #24991684, #24991686, #24991689, … |
| maximal quotient of | #25018307, #25018320, #25018341, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5504, 7778);