Finite Group DatabasebetaFinite Group Databasebeta| order | 1100 |
| isoclinism | isoclinic class of C11⋊#1035 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C11⋊#1035 |
| Fitting, derived, Hall | C11×C25 ⋊ C4 |
| Sylow | C25 ⋊ Dic11 |
| Sylow | C11 ⋊ #1035 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, hypocenter | C11×C25 | C4 |
| Frattini | C5 | C11⋊AGL(1,𝔽5) |
| socle | C5×C11 | AGL(1,𝔽5) |
| prime radical, cosocle | C11×D25 | C2 |
| LCS | G ▷ C11×C25 | |
| UCS | C1 | |
18 conjugacy classes of subgroups.
| minimal degree | μ(G) = 36 |
| transitive degree | μt(G) = 275 |
Polycyclic presentation:
2^2,5,11,5|a^2=b,c^5=e,c^a=c^2e,d^a=d^10,e^a=e^2,c^b=c^4e^4,e^b=e^480 conjugacy classes — view the full character table.
| maximal subgroup of | C3×C11⋊#1035, C3⋊(C11⋊#1035), C121⋊#1035, … |
| maximal normal subgroup of | C3×C11⋊#1035, C11×C11⋊#1035, C13×C11⋊#1035, … |
| maximal quotient of | C3×C11⋊#1035, C3⋊(C11⋊#1035), C121⋊#1035, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1100, 10);