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C5×C7×AGL(1,𝔽23) #31799325

order17710
isoclinismisoclinic class of AGL(1,𝔽23)
automorphism?
homologyAbelianization (H1) = C2×C5×C7×C11 · Schur multiplier (H2) = C1

Aliases

direct productC5×C7×AGL(1,𝔽23)
unambiguous semidirect productD23⋊(C5×C7×C11)
unambiguous semidirect product(C5×D23)⋊(C7×C11)
unambiguous semidirect product(C23⋊C11)⋊(C2×C5×C7)
unambiguous semidirect product(C7×D23)⋊(C5×C11)
unambiguous semidirect product(C5×C7×D23)⋊C11

Splittings

Fitting, socle, HallC5×C7×C23 ⋊ C2×C11
derived, SylowC23 ⋊ C2×C5×C7×C11
HallC5×C7×C23⋊C11 ⋊ C2
HallC7×C23⋊C11 ⋊ C2×C5
HallC5×C7×D23 ⋊ C11
HallC5×C23⋊C11 ⋊ C2×C7
HallC7×D23 ⋊ C5×C11
HallC23⋊C11 ⋊ C2×C5×C7
HallC5×D23 ⋊ C7×C11
HallC7×C23 ⋊ C2×C5×C11
HallC5×C23 ⋊ C2×C7×C11
HallD23 ⋊ C5×C7×C11

Subgroups

subgroupG/H
center, hypercenterC5×C7AGL(1,𝔽23)
commutator, cosocle, hypocenterC23C2×C5×C7×C11
FrattiniC1G
Fitting, socleC5×C7×C23C2×C11
LCSG ▷ C23
UCSC1 ◁ C5×C7

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 805

Conjugacy classes & character table

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

Relationships

maximal subgroup ofC5×D7×AGL(1,𝔽23), C7×D5×AGL(1,𝔽23), D35×AGL(1,𝔽23), …
maximal normal subgroup ofC5×D7×AGL(1,𝔽23), C7×D5×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, 19);