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C5×C49×AGL(1,𝔽11) #41003947

order26950
automorphism?
homologyAbelianization (H1) = C2×C52×C49 · Schur multiplier (H2) = C5

Aliases

direct productC5×C49×AGL(1,𝔽11)
unambiguous semidirect productD11⋊(C52×C49)
unambiguous semidirect product(C11⋊C5)⋊(C2×C5×C49)
unambiguous semidirect product(C5×D11)⋊(C5×C49)
unambiguous semidirect product(D11×C49)⋊C52
unambiguous semidirect product(C5×D11×C49)⋊C5

Splittings

FittingC5×C11×C49 ⋊ C2×C5
derived, SylowC11 ⋊ C2×C52×C49
HallC5×C49×C11⋊C5 ⋊ C2
HallD11×C49 ⋊ C52
HallC11×C49 ⋊ C2×C52
HallC5×C11⋊C5 ⋊ C2×C49
HallD11 ⋊ C52×C49

Subgroups

subgroupG/H
center, hypercenterC5×C49AGL(1,𝔽11)
commutator, hypocenterC11C2×C52×C49
FrattiniC7C5×C7×AGL(1,𝔽11)
FittingC5×C11×C49C2×C5
socleC5×C7×C11C2×C5×C7
prime radicalC5×C7×AGL(1,𝔽11)C7
cosocleC7×C11C2×C52×C7
LCSG ▷ C11
UCSC1 ◁ C5×C49

96 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2695

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(26950, 14);