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C2×C29×C3⋊AGL(1,𝔽7) #20300638

order7308
isoclinismisoclinic class of C3⋊AGL(1,𝔽7)
automorphism?
homologyAbelianization (H1) = C22×C3×C29 · Schur multiplier (H2) = C2

Aliases

direct productC2×C29×C3⋊AGL(1,𝔽7)
unambiguous semidirect product(C2×C3)⋊(C29×AGL(1,𝔽7))
unambiguous semidirect product(C2×ΓL(1,𝔽8))⋊(D3×C29)
unambiguous semidirect product(C2×D21)⋊(C3×C29)
unambiguous semidirect product(C2×C29×D21)⋊C3

Splittings

Fitting, socleC2×C3×C7×C29 ⋊ C2×C3
derivedC3×C7 ⋊ C22×C3×C29
HallC3×ΓL(1,𝔽8)×C29 ⋊ C22
HallC7×C29 ⋊ C2×C3×D3
HallC3×ΓL(1,𝔽8) ⋊ C22×C29
SylowC7 ⋊ C2×C3×D3×C29

Subgroups

subgroupG/H
center, hypercenterC2×C29C3⋊AGL(1,𝔽7)
commutator, hypocenterC3×C7C22×C3×C29
FrattiniC1G
Fitting, socleC2×C3×C7×C29C2×C3
LCSG ▷ C3×C7
UCSC1 ◁ C2×C29

88 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

696 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofD5×C29×C3⋊AGL(1,𝔽7), C2×C5×C29×C3⋊AGL(1,𝔽7), C2×C29×C3⋊(C5⋊AGL(1,𝔽7))
maximal normal subgroup ofC2×C5×C29×C3⋊AGL(1,𝔽7)
maximal quotient ofD5×C29×C3⋊AGL(1,𝔽7), C2×C5×C29×C3⋊AGL(1,𝔽7), C2×C29×C3⋊(C5⋊AGL(1,𝔽7))

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(7308, 113);