Finite Group Databasebeta

← Prev (#31799333) Next (#31799335) →

C7×C23⋊AGL(1,𝔽11) #31799334

order17710
automorphism?
homologyAbelianization (H1) = C2×C5×C7 · Schur multiplier (H2) = C1

Aliases

direct productC7×C23⋊AGL(1,𝔽11)
unambiguous semidirect productC23⋊(C7×AGL(1,𝔽11))
unambiguous semidirect product(C11⋊C5)⋊(C7×D23)
unambiguous semidirect productD253⋊(C5×C7)
unambiguous semidirect product(C7×D253)⋊C5

Splittings

Fitting, socle, HallC7×C11×C23 ⋊ C2×C5
derived, HallC11×C23 ⋊ C2×C5×C7
HallC7×C23×C11⋊C5 ⋊ C2
HallC7×D253 ⋊ C5
HallC23×C11⋊C5 ⋊ C2×C7
HallD253 ⋊ C5×C7
HallC7×C11⋊C5 ⋊ D23
HallC7×C23 ⋊ AGL(1,𝔽11)
HallC7×C11 ⋊ C5×D23
HallC11⋊C5 ⋊ C7×D23
SylowC23 ⋊ C7×AGL(1,𝔽11)
SylowC11 ⋊ C5×C7×D23

Subgroups

subgroupG/H
center, hypercenterC7C23⋊AGL(1,𝔽11)
commutator, cosocle, hypocenterC11×C23C2×C5×C7
FrattiniC1G
Fitting, socleC7×C11×C23C2×C5
LCSG ▷ C11×C23
UCSC1 ◁ C7

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1771

Conjugacy classes & character table

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

Relationships

maximal subgroup ofC7×D23×AGL(1,𝔽11), D7×C23⋊AGL(1,𝔽11), D161⋊AGL(1,𝔽11), …
maximal normal subgroup ofC7×D23×AGL(1,𝔽11), D7×C23⋊AGL(1,𝔽11), D161⋊AGL(1,𝔽11), …
maximal quotient ofC7×C23⋊(Dic11⋊C5), C2×C7×C23⋊AGL(1,𝔽11)

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(17710, 28);