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C3×ΓL(1,𝔽8)×C23⋊C11 #30629971

order15939
automorphism?
homologyAbelianization (H1) = C32×C11 · Schur multiplier (H2) = C3

Aliases

direct productC3×ΓL(1,𝔽8)×C23⋊C11
unambiguous semidirect productC7⋊(C32×C23⋊C11)
unambiguous semidirect product(C3×C7)⋊(C3×C23⋊C11)
unambiguous semidirect productC23⋊(C3×C11×ΓL(1,𝔽8))
unambiguous semidirect product(C3×C23)⋊(C11×ΓL(1,𝔽8))
unambiguous semidirect product(ΓL(1,𝔽8)×C23)⋊(C3×C11)
unambiguous semidirect product(C3×ΓL(1,𝔽8)×C23)⋊C11
unambiguous semidirect product(C7×C23⋊C11)⋊C32
unambiguous semidirect product(C3×C7×C23⋊C11)⋊C3

Splittings

Fitting, socleC3×C7×C23 ⋊ C3×C11
derived, HallC7×C23 ⋊ C32×C11
HallC7×C23⋊C11 ⋊ C32
HallC3×ΓL(1,𝔽8)×C23 ⋊ C11
SylowC23 ⋊ C3×C11×ΓL(1,𝔽8)
SylowC7 ⋊ C32×C23⋊C11

Subgroups

subgroupG/H
center, hypercenterC3ΓL(1,𝔽8)×C23⋊C11
commutator, cosocle, hypocenterC7×C23C32×C11
FrattiniC1G
Fitting, socleC3×C7×C23C3×C11
LCSG ▷ C7×C23
UCSC1 ◁ C3

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 483

Conjugacy classes & character table

195 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC3×ΓL(1,𝔽8)⋊AGL(1,𝔽23), C3×AGL(1,𝔽7)×C23⋊C11, C3×ΓL(1,𝔽8)×AGL(1,𝔽23), …
maximal normal subgroup ofC3×ΓL(1,𝔽8)⋊AGL(1,𝔽23), C3×AGL(1,𝔽7)×C23⋊C11, C3×ΓL(1,𝔽8)×AGL(1,𝔽23), …
maximal quotient ofC2×C3×ΓL(1,𝔽8)×C23⋊C11

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15939, 6);