Finite Group Databasebeta

← Prev (#24924705) Next (#24924707) →

C11×AGL(1,𝔽5)×C49 #24924706

order10780
isoclinismisoclinic class of AGL(1,𝔽5)
automorphism?
homologyAbelianization (H1) = C4×C11×C49 · Schur multiplier (H2) = C1

Aliases

direct productC11×AGL(1,𝔽5)×C49

Splittings

Fitting, HallC5×C11×C49 ⋊ C4
derived, SylowC5 ⋊ C4×C11×C49
HallC5×C49 ⋊ C4×C11
HallC5×C11 ⋊ C4×C49

Subgroups

subgroupG/H
center, hypercenterC11×C49AGL(1,𝔽5)
commutator, hypocenterC5C4×C11×C49
FrattiniC7C7×C11×AGL(1,𝔽5)
FittingC5×C11×C49C4
socleC5×C7×C11C4×C7
prime radicalC7×D5×C11C2×C7
cosocleC7×D5C2×C7×C11
LCSG ▷ C5
UCSC1 ◁ C11×C49

36 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

2695 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC11×AGL(1,𝔽5)×C49⋊C3, C3×C11×AGL(1,𝔽5)×C49, C11×C49×ΓL(1,𝔽16)
maximal normal subgroup ofC11×AGL(1,𝔽5)×C49⋊C3, C3×C11×AGL(1,𝔽5)×C49
maximal quotient ofC3×C11×AGL(1,𝔽5)×C49, C11×C49×ΓL(1,𝔽16)

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(10780, 19);