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C7×C5⋊AGL(1,𝔽23) #31799329

order17710
automorphism?
homologyAbelianization (H1) = C2×C7×C11 · Schur multiplier (H2) = C1

Aliases

direct productC7×C5⋊AGL(1,𝔽23)
unambiguous semidirect productC5⋊(C7×AGL(1,𝔽23))
unambiguous semidirect productD115⋊(C7×C11)
unambiguous semidirect product(C23⋊C11)⋊(C7×D5)
unambiguous semidirect product(C7×D115)⋊C11

Splittings

Fitting, socle, HallC5×C7×C23 ⋊ C2×C11
derived, HallC5×C23 ⋊ C2×C7×C11
HallC5×C7×C23⋊C11 ⋊ C2
HallC7×C23⋊C11 ⋊ D5
HallC7×D115 ⋊ C11
HallC5×C23⋊C11 ⋊ C2×C7
HallC23⋊C11 ⋊ C7×D5
HallD115 ⋊ C7×C11
HallC7×C23 ⋊ D5×C11
HallC5×C7 ⋊ AGL(1,𝔽23)
SylowC23 ⋊ C7×D5×C11
SylowC5 ⋊ C7×AGL(1,𝔽23)

Subgroups

subgroupG/H
center, hypercenterC7C5⋊AGL(1,𝔽23)
commutator, cosocle, hypocenterC5×C23C2×C7×C11
FrattiniC1G
Fitting, socleC5×C7×C23C2×C11
LCSG ▷ C5×C23
UCSC1 ◁ C7

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 805

Conjugacy classes & character table

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

Relationships

maximal subgroup ofC7×D5×AGL(1,𝔽23), D7×C5⋊AGL(1,𝔽23), D35⋊AGL(1,𝔽23), …
maximal normal subgroup ofC7×D5×AGL(1,𝔽23), D7×C5⋊AGL(1,𝔽23), D35⋊AGL(1,𝔽23), …
maximal quotient ofC7×(C23⋊C11)⋊Dic5, C2×C7×C5⋊AGL(1,𝔽23)

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(17710, 23);