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C5×C7⋊(C7⋊AGL(1,𝔽11)) #41003988

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

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 product(C7⋊D77)⋊C52
unambiguous semidirect product(C5×C7⋊D77)⋊C5

Splittings

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

Subgroups

subgroupG/H
center, hypercenterC5C7⋊(C7⋊AGL(1,𝔽11))
commutator, cosocle, hypocenterC72×C11C2×C52
FrattiniC1G
Fitting, socleC5×C72×C11C2×C5
LCSG ▷ C72×C11
UCSC1 ◁ C5

320 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2695

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(26950, 55);