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C23×C7⋊AGL(1,𝔽11) #31799337

order17710
automorphism?
homologyAbelianization (H1) = C2×C5×C23 · Schur multiplier (H2) = C1

Aliases

direct productC23×C7⋊AGL(1,𝔽11)
unambiguous semidirect productC7⋊(C23×AGL(1,𝔽11))
unambiguous semidirect product(C11⋊C5)⋊(D7×C23)
unambiguous semidirect productD77⋊(C5×C23)
unambiguous semidirect product(C23×D77)⋊C5

Splittings

Fitting, socle, HallC7×C11×C23 ⋊ C2×C5
derived, HallC7×C11 ⋊ C2×C5×C23
HallC7×C23×C11⋊C5 ⋊ C2
HallC23×D77 ⋊ C5
HallC23×C11⋊C5 ⋊ D7
HallC7×C11⋊C5 ⋊ C2×C23
HallC11×C23 ⋊ C5×D7
HallC7×C23 ⋊ AGL(1,𝔽11)
HallD77 ⋊ C5×C23
HallC11⋊C5 ⋊ D7×C23
SylowC11 ⋊ C5×D7×C23
SylowC7 ⋊ C23×AGL(1,𝔽11)

Subgroups

subgroupG/H
center, hypercenterC23C7⋊AGL(1,𝔽11)
commutator, cosocle, hypocenterC7×C11C2×C5×C23
FrattiniC1G
Fitting, socleC7×C11×C23C2×C5
LCSG ▷ C7×C11
UCSC1 ◁ C23

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1771

Conjugacy classes & character table

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

Relationships

maximal subgroup ofD23×C7⋊AGL(1,𝔽11), D7×C23×AGL(1,𝔽11), D161⋊AGL(1,𝔽11), …
maximal normal subgroup ofD23×C7⋊AGL(1,𝔽11), D7×C23×AGL(1,𝔽11), D161⋊AGL(1,𝔽11), …
maximal quotient ofC23×C7⋊(Dic11⋊C5), C2×C23×C7⋊AGL(1,𝔽11)

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(17710, 31);