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C7×C5⋊(C7⋊AGL(1,𝔽11)) #41003992

order26950
automorphism?
homologyAbelianization (H1) = C2×C5×C7 · Schur multiplier (H2) = C1

Aliases

direct productC7×C5⋊(C7⋊AGL(1,𝔽11))
unambiguous semidirect productC5⋊(C7×C7⋊AGL(1,𝔽11))
unambiguous semidirect productC7⋊(C7×C5⋊AGL(1,𝔽11))
unambiguous semidirect product(C11⋊C5)⋊(C7×D35)
unambiguous semidirect productD385⋊(C5×C7)
unambiguous semidirect product(C7×D385)⋊C5

Splittings

Fitting, socleC5×C72×C11 ⋊ C2×C5
derivedC5×C7×C11 ⋊ C2×C5×C7
HallC5×C72×C11⋊C5 ⋊ C2
HallC72×C11 ⋊ C5×D5
HallC5×C11⋊C5 ⋊ C7×D7
SylowC72 ⋊ C5⋊AGL(1,𝔽11)
SylowC11 ⋊ C5×C7×D35

Subgroups

subgroupG/H
center, hypercenterC7C5⋊(C7⋊AGL(1,𝔽11))
commutator, cosocle, hypocenterC5×C7×C11C2×C5×C7
FrattiniC1G
Fitting, socleC5×C72×C11C2×C5
LCSG ▷ C5×C7×C11
UCSC1 ◁ C7

128 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 770

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(26950, 59);