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C3×C7×AGL(1,𝔽23) #24922312

order10626
isoclinismisoclinic class of AGL(1,𝔽23)
automorphism?
homologyAbelianization (H1) = C2×C3×C7×C11 · Schur multiplier (H2) = C1

Aliases

direct productC3×C7×AGL(1,𝔽23)
unambiguous semidirect productD23⋊(C3×C7×C11)
unambiguous semidirect product(C3×D23)⋊(C7×C11)
unambiguous semidirect product(C23⋊C11)⋊(C2×C3×C7)
unambiguous semidirect product(C3×C7×D23)⋊C11

Splittings

Fitting, socle, HallC3×C7×C23 ⋊ C2×C11
derived, SylowC23 ⋊ C2×C3×C7×C11
HallC3×C7×C23⋊C11 ⋊ C2
HallC7×C23⋊C11 ⋊ C2×C3
HallC3×C7×D23 ⋊ C11
HallC3×C23⋊C11 ⋊ C2×C7
HallC7×D23 ⋊ C3×C11
HallC23⋊C11 ⋊ C2×C3×C7
HallC7×C23 ⋊ C2×C3×C11
HallC3×D23 ⋊ C7×C11
HallC3×C23 ⋊ C2×C7×C11
HallD23 ⋊ C3×C7×C11

Subgroups

subgroupG/H
center, hypercenterC3×C7AGL(1,𝔽23)
commutator, cosocle, hypocenterC23C2×C3×C7×C11
FrattiniC1G
Fitting, socleC3×C7×C23C2×C11
LCSG ▷ C23
UCSC1 ◁ C3×C7

32 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

483 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC3×D7×AGL(1,𝔽23), D3×C7×AGL(1,𝔽23), D21×AGL(1,𝔽23), …
maximal normal subgroup ofC3×D7×AGL(1,𝔽23), D3×C7×AGL(1,𝔽23), D21×AGL(1,𝔽23), …
maximal quotient ofC3×C7×Dic23⋊C11, C2×C3×C7×AGL(1,𝔽23), C7×C9×AGL(1,𝔽23), …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(10626, 20);