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C2×C5⋊AGL(1,𝔽23) #19099435

order5060
automorphism?
homologyAbelianization (H1) = C22×C11 · Schur multiplier (H2) = C2

Aliases

direct productC2×C5⋊AGL(1,𝔽23)
unambiguous semidirect product(C2×C5)⋊AGL(1,𝔽23)
unambiguous semidirect product(C2×D115)⋊C11
unambiguous semidirect product(C2×C23⋊C11)⋊D5

Splittings

Fitting, socleC2×C5×C23 ⋊ C2×C11
derived, HallC5×C23 ⋊ C22×C11
HallC5×C23⋊C11 ⋊ C22
HallC2×D115 ⋊ C11
HallC23⋊C11 ⋊ C2×D5
SylowC23 ⋊ C2×D5×C11
SylowC5 ⋊ C2×AGL(1,𝔽23)

Subgroups

subgroupG/H
center, hypercenterC2C5⋊AGL(1,𝔽23)
commutator, hypocenterC5×C23C22×C11
FrattiniC1G
Fitting, socleC2×C5×C23C2×C11
LCSG ▷ C5×C23
UCSC1 ◁ C2

40 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

98 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofD3×C5⋊AGL(1,𝔽23), C2×C3×C5⋊AGL(1,𝔽23), C2×C3⋊(C5⋊AGL(1,𝔽23)), …
maximal normal subgroup ofC2×C3×C5⋊AGL(1,𝔽23), C2×C5×C5⋊AGL(1,𝔽23), C2×C7×C5⋊AGL(1,𝔽23), …
maximal quotient ofD3×C5⋊AGL(1,𝔽23), C2×C3×C5⋊AGL(1,𝔽23), C2×C3⋊(C5⋊AGL(1,𝔽23)), …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(5060, 22);