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C7×C3⋊AGL(1,𝔽23) #24922316

order10626
automorphism?
homologyAbelianization (H1) = C2×C7×C11 · Schur multiplier (H2) = C1

Aliases

direct productC7×C3⋊AGL(1,𝔽23)
unambiguous semidirect productC3⋊(C7×AGL(1,𝔽23))
unambiguous semidirect productD69⋊(C7×C11)
unambiguous semidirect product(C23⋊C11)⋊(D3×C7)
unambiguous semidirect product(C7×D69)⋊C11

Splittings

Fitting, socle, HallC3×C7×C23 ⋊ C2×C11
derived, HallC3×C23 ⋊ C2×C7×C11
HallC3×C7×C23⋊C11 ⋊ C2
HallC7×C23⋊C11 ⋊ D3
HallC7×D69 ⋊ C11
HallC3×C23⋊C11 ⋊ C2×C7
HallC23⋊C11 ⋊ D3×C7
HallC7×C23 ⋊ D3×C11
HallD69 ⋊ C7×C11
SylowC23 ⋊ D3×C7×C11
HallC3×C7 ⋊ AGL(1,𝔽23)
SylowC3 ⋊ C7×AGL(1,𝔽23)

Subgroups

subgroupG/H
center, hypercenterC7C3⋊AGL(1,𝔽23)
commutator, cosocle, hypocenterC3×C23C2×C7×C11
FrattiniC1G
Fitting, socleC3×C7×C23C2×C11
LCSG ▷ C3×C23
UCSC1 ◁ C7

32 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

252 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofD3×C7×AGL(1,𝔽23), D7×C3⋊AGL(1,𝔽23), D21⋊AGL(1,𝔽23), …
maximal normal subgroup ofD3×C7×AGL(1,𝔽23), D7×C3⋊AGL(1,𝔽23), D21⋊AGL(1,𝔽23), …
maximal quotient ofC7×C3⋊(Dic23⋊C11), C2×C7×C3⋊AGL(1,𝔽23), C7×C9⋊AGL(1,𝔽23), …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(10626, 24);