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C3×C7×ΓL(1,𝔽8)×C43 #34038944

order18963
automorphism?
homologyAbelianization (H1) = C32×C7×C43 · Schur multiplier (H2) = C3

Aliases

direct productC3×C7×ΓL(1,𝔽8)×C43
unambiguous semidirect productC7⋊(C32×C7×C43)
unambiguous semidirect product(C3×C7)⋊(C3×C7×C43)

Splittings

Fitting, socleC3×C72×C43 ⋊ C3
derivedC7 ⋊ C32×C7×C43
HallC72×C43 ⋊ C32
SylowC72 ⋊ C32×C43

Subgroups

subgroupG/H
center, hypercenterC3×C7×C43ΓL(1,𝔽8)
commutator, cosocle, hypocenterC7C32×C7×C43
FrattiniC1G
Fitting, socleC3×C72×C43C3
LCSG ▷ C7
UCSC1 ◁ C3×C7×C43

56 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2709

Conjugacy classes & character table

4515 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC3×C7×ΓL(1,𝔽8)×D43, C3×C7×AGL(1,𝔽7)×C43, C3×C7×ΓL(1,𝔽8)⋊D43, …
maximal normal subgroup ofC3×C7×ΓL(1,𝔽8)×D43, C3×C7×AGL(1,𝔽7)×C43, C3×C7×ΓL(1,𝔽8)⋊D43, …
maximal quotient ofC2×C3×C7×ΓL(1,𝔽8)×C43

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(18963, 51);