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C7×C13⋊AGL(1,𝔽11) #23756334

order10010
automorphism?
homologyAbelianization (H1) = C2×C5×C7 · Schur multiplier (H2) = C1

Aliases

direct productC7×C13⋊AGL(1,𝔽11)
unambiguous semidirect productC13⋊(C7×AGL(1,𝔽11))
unambiguous semidirect product(C11⋊C5)⋊(C7×D13)
unambiguous semidirect productD143⋊(C5×C7)
unambiguous semidirect product(C7×D143)⋊C5

Splittings

Fitting, socle, HallC7×C11×C13 ⋊ C2×C5
derived, HallC11×C13 ⋊ C2×C5×C7
HallC7×C13×C11⋊C5 ⋊ C2
HallC7×D143 ⋊ C5
HallC13×C11⋊C5 ⋊ C2×C7
HallC7×C11⋊C5 ⋊ D13
HallD143 ⋊ C5×C7
HallC7×C13 ⋊ AGL(1,𝔽11)
HallC7×C11 ⋊ C5×D13
HallC11⋊C5 ⋊ C7×D13
SylowC13 ⋊ C7×AGL(1,𝔽11)
SylowC11 ⋊ C5×C7×D13

Subgroups

subgroupG/H
center, hypercenterC7C13⋊AGL(1,𝔽11)
commutator, cosocle, hypocenterC11×C13C2×C5×C7
FrattiniC1G
Fitting, socleC7×C11×C13C2×C5
LCSG ▷ C11×C13
UCSC1 ◁ C7

32 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

371 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC7×D13×AGL(1,𝔽11), D7×C13⋊AGL(1,𝔽11), D91⋊AGL(1,𝔽11), …
maximal normal subgroup ofC7×D13×AGL(1,𝔽11), D7×C13⋊AGL(1,𝔽11), D91⋊AGL(1,𝔽11), …
maximal quotient ofC7×(C11⋊C5)⋊Dic13, C2×C7×C13⋊AGL(1,𝔽11), C3×C7×C13⋊AGL(1,𝔽11), …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(10010, 20);