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C2×AGL(1,𝔽7)×C43⋊C7 #38760384

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

Aliases

direct productC2×AGL(1,𝔽7)×C43⋊C7
unambiguous semidirect productD7⋊(C2×C3×C43⋊C7)
unambiguous semidirect productΓL(1,𝔽8)⋊(C22×C43⋊C7)
unambiguous semidirect product(C2×D7)⋊(C3×C43⋊C7)
unambiguous semidirect product(C2×ΓL(1,𝔽8))⋊(C2×C43⋊C7)
unambiguous semidirect product(C2×AGL(1,𝔽7)×C43)⋊C7

Splittings

Fitting, socleC2×C7×C43 ⋊ C2×C3×C7
derivedC7×C43 ⋊ C22×C3×C7
HallC2×D7×C43⋊C7 ⋊ C3
HallΓL(1,𝔽8)×C43⋊C7 ⋊ C22
HallC7×C43⋊C7 ⋊ C22×C3
SylowC43 ⋊ C2×C7×AGL(1,𝔽7)

Subgroups

subgroupG/H
center, hypercenterC2AGL(1,𝔽7)×C43⋊C7
commutator, cosocle, hypocenterC7×C43C22×C3×C7
FrattiniC1G
Fitting, socleC2×C7×C43C2×C3×C7
LCSG ▷ C7×C43
UCSC1 ◁ C2

84 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 602

Conjugacy classes & character table

182 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(25284, 191);