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C49×C5⋊AGL(1,𝔽11) #41003950

order26950
automorphism?
homologyAbelianization (H1) = C2×C5×C49 · Schur multiplier (H2) = C1

Aliases

direct productC49×C5⋊AGL(1,𝔽11)
unambiguous semidirect productC5⋊(C49×AGL(1,𝔽11))
unambiguous semidirect product(C11⋊C5)⋊(D5×C49)
unambiguous semidirect productD55⋊(C5×C49)
unambiguous semidirect product(C49×D55)⋊C5

Splittings

FittingC5×C11×C49 ⋊ C2×C5
derivedC5×C11 ⋊ C2×C5×C49
HallC5×C49×C11⋊C5 ⋊ C2
HallC11×C49 ⋊ C5×D5
HallC5×C11⋊C5 ⋊ C2×C49
SylowC11 ⋊ C5×D5×C49

Subgroups

subgroupG/H
center, hypercenterC49C5⋊AGL(1,𝔽11)
commutator, hypocenterC5×C11C2×C5×C49
FrattiniC7C7×C5⋊AGL(1,𝔽11)
FittingC5×C11×C49C2×C5
socle, cosocleC5×C7×C11C2×C5×C7
prime radicalC7×C5⋊AGL(1,𝔽11)C7
LCSG ▷ C5×C11
UCSC1 ◁ C49

60 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2695

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(26950, 17);