Finite Group Databasebeta

← Prev (#31799326) Next (#31799328) →

C5×C7⋊AGL(1,𝔽23) #31799327

order17710
automorphism?
homologyAbelianization (H1) = C2×C5×C11 · Schur multiplier (H2) = C1

Aliases

direct productC5×C7⋊AGL(1,𝔽23)
unambiguous semidirect productC7⋊(C5×AGL(1,𝔽23))
unambiguous semidirect product(C23⋊C11)⋊(C5×D7)
unambiguous semidirect productD161⋊(C5×C11)
unambiguous semidirect product(C5×D161)⋊C11

Splittings

Fitting, socle, HallC5×C7×C23 ⋊ C2×C11
derived, HallC7×C23 ⋊ C2×C5×C11
HallC5×C7×C23⋊C11 ⋊ C2
HallC7×C23⋊C11 ⋊ C2×C5
HallC5×D161 ⋊ C11
HallC5×C23⋊C11 ⋊ D7
HallD161 ⋊ C5×C11
HallC23⋊C11 ⋊ C5×D7
HallC5×C23 ⋊ C11×D7
HallC5×C7 ⋊ AGL(1,𝔽23)
SylowC23 ⋊ C5×C11×D7
SylowC7 ⋊ C5×AGL(1,𝔽23)

Subgroups

subgroupG/H
center, hypercenterC5C7⋊AGL(1,𝔽23)
commutator, cosocle, hypocenterC7×C23C2×C5×C11
FrattiniC1G
Fitting, socleC5×C7×C23C2×C11
LCSG ▷ C7×C23
UCSC1 ◁ C5

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 805

Conjugacy classes & character table

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

Relationships

maximal subgroup ofC5×D7×AGL(1,𝔽23), D5×C7⋊AGL(1,𝔽23), D35⋊AGL(1,𝔽23), …
maximal normal subgroup ofC5×D7×AGL(1,𝔽23), D5×C7⋊AGL(1,𝔽23), D35⋊AGL(1,𝔽23), …
maximal quotient ofC5×C7⋊(Dic23⋊C11), C2×C5×C7⋊AGL(1,𝔽23)

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(17710, 21);