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C2×C5×AGL(1,𝔽23) #19099434

order5060
isoclinismisoclinic class of AGL(1,𝔽23)
automorphism?
homologyAbelianization (H1) = C22×C5×C11 · Schur multiplier (H2) = C2

Aliases

direct productC2×C5×AGL(1,𝔽23)
unambiguous semidirect productD23⋊(C2×C5×C11)
unambiguous semidirect product(C2×D23)⋊(C5×C11)
unambiguous semidirect product(C23⋊C11)⋊(C22×C5)
unambiguous semidirect product(C2×C5×D23)⋊C11
unambiguous semidirect product(C2×C23⋊C11)⋊(C2×C5)

Splittings

Fitting, socleC2×C5×C23 ⋊ C2×C11
derived, SylowC23 ⋊ C22×C5×C11
HallC5×C23⋊C11 ⋊ C22
HallC2×C5×D23 ⋊ C11
HallC23⋊C11 ⋊ C22×C5
HallC5×C23 ⋊ C22×C11
HallC2×D23 ⋊ C5×C11

Subgroups

subgroupG/H
center, hypercenterC2×C5AGL(1,𝔽23)
commutator, hypocenterC23C22×C5×C11
FrattiniC1G
Fitting, socleC2×C5×C23C2×C11
LCSG ▷ C23
UCSC1 ◁ C2×C5

40 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

230 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC5×D3×AGL(1,𝔽23), C2×C3×C5×AGL(1,𝔽23), C2×C5×C3⋊AGL(1,𝔽23), …
maximal normal subgroup ofC2×C3×C5×AGL(1,𝔽23), C2×C25×AGL(1,𝔽23), C2×C52×AGL(1,𝔽23), …
maximal quotient ofC5×D3×AGL(1,𝔽23), C2×C3×C5×AGL(1,𝔽23), C2×C5×C3⋊AGL(1,𝔽23), …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(5060, 21);