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C49×C11⋊AGL(1,𝔽5) #24924707

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

Aliases

direct productC49×C11⋊AGL(1,𝔽5)
unambiguous semidirect productC11⋊(AGL(1,𝔽5)×C49)

Splittings

Fitting, HallC5×C11×C49 ⋊ C4
derived, HallC5×C11 ⋊ C4×C49
HallC11×C49 ⋊ AGL(1,𝔽5)
HallC5×C49 ⋊ Dic11
SylowC11 ⋊ AGL(1,𝔽5)×C49
SylowC5 ⋊ Dic11×C49

Subgroups

subgroupG/H
center, hypercenterC49C11⋊AGL(1,𝔽5)
commutator, hypocenterC5×C11C4×C49
FrattiniC7C7×C11⋊AGL(1,𝔽5)
FittingC5×C11×C49C4
socleC5×C7×C11C4×C7
prime radical, cosocleC7×D5×C11C2×C7
LCSG ▷ C5×C11
UCSC1 ◁ C49

36 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1225 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC49⋊C3×C11⋊AGL(1,𝔽5), C3×C49×C11⋊AGL(1,𝔽5), C49×C3⋊(C11⋊AGL(1,𝔽5))
maximal normal subgroup ofC49⋊C3×C11⋊AGL(1,𝔽5), C3×C49×C11⋊AGL(1,𝔽5)
maximal quotient ofC3×C49×C11⋊AGL(1,𝔽5), C49×C3⋊(C11⋊AGL(1,𝔽5))

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(10780, 20);