Finite Group DatabasebetaFinite Group Databasebeta| order | 2180 |
| isoclinism | isoclinic class of #14546128 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Fitting, socle, derived, Hall | C5×C109 ⋊ C4 |
| Sylow | C109 ⋊ AGL(1,𝔽5) |
| Sylow | C5 ⋊ Dic109 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C5×C109 | C4 |
| prime radical, cosocle | D5×C109 | C2 |
| LCS | G ▷ C5×C109 | |
| UCS | C1 | |
12 conjugacy classes of subgroups.
| minimal degree | μ(G) = 114 |
| transitive degree | μt(G) = 545 |
Polycyclic presentation:
2^2,5,109|a^2=b,c^a=c^2,d^a=d^108,c^b=c^4221 conjugacy classes — view the full character table.
| maximal subgroup of | #24926249, C5×#14546128, #24926272, … |
| maximal normal subgroup of | C5×#14546128, C7×#14546128, C11×#14546128, … |
| maximal quotient of | #24926249, C5×#14546128, #24926272, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2180, 10);