Finite Group DatabasebetaFinite Group Databasebeta| order | 5540 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Fitting, socle, derived, Hall | C5×C277 ⋊ C4 |
| Sylow | C277 ⋊ AGL(1,𝔽5) |
| Sylow | C5 ⋊ Dic277 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C5×C277 | C4 |
| LCS | G ▷ C5×C277 | |
| UCS | C1 | |
12 conjugacy classes of subgroups.
Polycyclic presentation:
2^2,5,277|a^2=b,c^a=c^2,d^a=d^276,c^b=c^4557 conjugacy classes — view the full character table.
| maximal subgroup of | #19149795⋊C3, C3×#19149795, C3⋊#19149795, … |
| maximal normal subgroup of | #19149795⋊C3, C3×#19149795, C5×#19149795 |
| maximal quotient of | C3×#19149795, C3⋊#19149795, #42121175, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5540, 10);