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C13×C7⋊AGL(1,𝔽11) #23756337

order10010
automorphism?
homologyAbelianization (H1) = C2×C5×C13 · Schur multiplier (H2) = C1

Aliases

direct productC13×C7⋊AGL(1,𝔽11)
unambiguous semidirect productC7⋊(C13×AGL(1,𝔽11))
unambiguous semidirect product(C11⋊C5)⋊(C13×D7)
unambiguous semidirect productD77⋊(C5×C13)
unambiguous semidirect product(C13×D77)⋊C5

Splittings

Fitting, socle, HallC7×C11×C13 ⋊ C2×C5
derived, HallC7×C11 ⋊ C2×C5×C13
HallC7×C13×C11⋊C5 ⋊ C2
HallC13×D77 ⋊ C5
HallC13×C11⋊C5 ⋊ D7
HallC7×C11⋊C5 ⋊ C2×C13
HallD77 ⋊ C5×C13
HallC11×C13 ⋊ C5×D7
HallC7×C13 ⋊ AGL(1,𝔽11)
HallC11⋊C5 ⋊ C13×D7
SylowC11 ⋊ C5×C13×D7
SylowC7 ⋊ C13×AGL(1,𝔽11)

Subgroups

subgroupG/H
center, hypercenterC13C7⋊AGL(1,𝔽11)
commutator, cosocle, hypocenterC7×C11C2×C5×C13
FrattiniC1G
Fitting, socleC7×C11×C13C2×C5
LCSG ▷ C7×C11
UCSC1 ◁ C13

32 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

416 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofD13×C7⋊AGL(1,𝔽11), C13×D7×AGL(1,𝔽11), D91⋊AGL(1,𝔽11), …
maximal normal subgroup ofD13×C7⋊AGL(1,𝔽11), C13×D7×AGL(1,𝔽11), D91⋊AGL(1,𝔽11), …
maximal quotient ofC13×C7⋊(Dic11⋊C5), C2×C13×C7⋊AGL(1,𝔽11), C3×C13×C7⋊AGL(1,𝔽11), …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(10010, 23);