Finite Group DatabasebetaFinite Group Databasebeta| order | 1100 |
| isoclinism | isoclinic class of C11⋊#1044 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C5 |
| unambiguous semidirect product | C11⋊#1044 |
| Fitting, socle, derived, Hall | C52×C11 ⋊ C4 |
| Sylow | C52 ⋊ Dic11 |
| Sylow | C11 ⋊ #1044 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C52×C11 | C4 |
| prime radical, cosocle | C11×C5⋊D5 | C2 |
| LCS | G ▷ C52×C11 | |
| UCS | C1 | |
32 conjugacy classes of subgroups.
| transitive degree | μt(G) = 110 |
Polycyclic presentation:
2^2,5^2,11|a^2=b,c^a=c^3,d^a=d^2,e^a=e^10,c^b=c^4,d^b=d^480 conjugacy classes — view the full character table.
| maximal subgroup of | C11⋊#64480, C3×C11⋊#1044, C3⋊(C11⋊#1044), … |
| maximal normal subgroup of | C3×C11⋊#1044, C11×C11⋊#1044, C13×C11⋊#1044, … |
| maximal quotient of | C3×C11⋊#1044, C3⋊(C11⋊#1044), C121⋊#1044, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1100, 38);