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C2×C7×AGL(1,𝔽43) #38760378

order25284
automorphism?
homologyAbelianization (H1) = C22×C3×C72 · Schur multiplier (H2) = C2×C7

Aliases

direct productC2×C7×AGL(1,𝔽43)
unambiguous semidirect product(D43⋊C3)⋊(C2×C72)
unambiguous semidirect product(C2×D43⋊C3)⋊C72
unambiguous semidirect product(D43⋊C7)⋊(C2×C3×C7)
unambiguous semidirect product((C43⋊C3)⋊C7)⋊(C22×C7)
unambiguous semidirect product(C2×D43⋊C7)⋊(C3×C7)
unambiguous semidirect product(C2×(C43⋊C3)⋊C7)⋊(C2×C7)
unambiguous semidirect product(C2×C7×D43⋊C3)⋊C7

Splittings

Fitting, socleC2×C7×C43 ⋊ C2×C3×C7
derived, SylowC43 ⋊ C22×C3×C72
HallC2×C7×D43⋊C7 ⋊ C3
HallC7×(C43⋊C3)⋊C7 ⋊ C22
HallC7×C43⋊C7 ⋊ C22×C3
HallC2×D43⋊C3 ⋊ C72
HallC2×D43 ⋊ C3×C72
HallC43⋊C3 ⋊ C22×C72

Subgroups

subgroupG/H
center, hypercenterC2×C7AGL(1,𝔽43)
commutator, cosocle, hypocenterC43C22×C3×C72
FrattiniC1G
Fitting, socleC2×C7×C43C2×C3×C7
LCSG ▷ C43
UCSC1 ◁ C2×C7

200 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 602

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(25284, 185);