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C5×C7×C7⋊AGL(1,𝔽11) #41003986

order26950
automorphism?
homologyAbelianization (H1) = C2×C52×C7 · Schur multiplier (H2) = C5

Aliases

direct productC5×C7×C7⋊AGL(1,𝔽11)
unambiguous semidirect productC7⋊(C5×C7×AGL(1,𝔽11))
unambiguous semidirect product(C11⋊C5)⋊(C5×C7×D7)
unambiguous semidirect productD77⋊(C52×C7)
unambiguous semidirect product(C5×D77)⋊(C5×C7)
unambiguous semidirect product(C7×D77)⋊C52
unambiguous semidirect product(C5×C7×D77)⋊C5

Splittings

Fitting, socleC5×C72×C11 ⋊ C2×C5
derivedC7×C11 ⋊ C2×C52×C7
HallC5×C72×C11⋊C5 ⋊ C2
HallC7×D77 ⋊ C52
HallC72×C11 ⋊ C2×C52
HallC5×C11⋊C5 ⋊ C7×D7
SylowC72 ⋊ C5×AGL(1,𝔽11)
SylowC11 ⋊ C52×C7×D7

Subgroups

subgroupG/H
center, hypercenterC5×C7C7⋊AGL(1,𝔽11)
commutator, cosocle, hypocenterC7×C11C2×C52×C7
FrattiniC1G
Fitting, socleC5×C72×C11C2×C5
LCSG ▷ C7×C11
UCSC1 ◁ C5×C7

176 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 770

Conjugacy classes & character table

1120 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(26950, 53);