Finite Group DatabasebetaFinite Group Databasebeta| order | 10820 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Fitting, socle, derived, Hall | C5×C541 ⋊ C4 |
| Sylow | C541 ⋊ AGL(1,𝔽5) |
| Sylow | C5 ⋊ #14524194 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C5×C541 | C4 |
| prime radical, cosocle | D2705 | C2 |
| LCS | G ▷ C5×C541 | |
| UCS | C1 | |
12 conjugacy classes of subgroups.
Polycyclic presentation:
2^2,5,541|a^2=b,c^a=c^2,d^a=d^52,c^b=c^4,d^b=d^540680 conjugacy classes — view the full character table.
| maximal subgroup of | #24925267⋊C3, C3×#24925267, C3⋊#24925267 |
| maximal normal subgroup of | #24925267⋊C3, C3×#24925267 |
| maximal quotient of | C3×#24925267, C3⋊#24925267 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10820, 14);