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C2×C7×AGL(1,𝔽7)×C53 #44528425

order31164
automorphism?
homologyAbelianization (H1) = C22×C3×C7×C53 · Schur multiplier (H2) = C2

Aliases

direct productC2×C7×AGL(1,𝔽7)×C53
unambiguous semidirect productD7⋊(C2×C3×C7×C53)
unambiguous semidirect productΓL(1,𝔽8)⋊(C22×C7×C53)
unambiguous semidirect product(C2×D7)⋊(C3×C7×C53)
unambiguous semidirect product(C2×ΓL(1,𝔽8))⋊(C2×C7×C53)
unambiguous semidirect product(C2×D7×C53)⋊(C3×C7)

Splittings

Fitting, socleC2×C72×C53 ⋊ C2×C3
derivedC7 ⋊ C22×C3×C7×C53
HallC2×C7×D7×C53 ⋊ C3
HallC7×ΓL(1,𝔽8)×C53 ⋊ C22
HallC72×C53 ⋊ C22×C3
HallC2×C7×D7 ⋊ C3×C53
HallC7×ΓL(1,𝔽8) ⋊ C22×C53
SylowC72 ⋊ C22×C3×C53

Subgroups

subgroupG/H
center, hypercenterC2×C7×C53AGL(1,𝔽7)
commutator, cosocle, hypocenterC7C22×C3×C7×C53
FrattiniC1G
Fitting, socleC2×C72×C53C2×C3
LCSG ▷ C7
UCSC1 ◁ C2×C7×C53

84 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 4452

Conjugacy classes & character table

5194 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31164, 117);