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C3×AGL(1,𝔽7)×C67 #22554744

order8442
isoclinismisoclinic class of AGL(1,𝔽7)
automorphism?
homologyAbelianization (H1) = C2×C32×C67 · Schur multiplier (H2) = C3

Aliases

direct productC3×AGL(1,𝔽7)×C67
unambiguous semidirect productD7⋊(C32×C67)
unambiguous semidirect productΓL(1,𝔽8)⋊(C2×C3×C67)
unambiguous semidirect product(C3×D7)⋊(C3×C67)

Splittings

Fitting, socleC3×C7×C67 ⋊ C2×C3
derived, SylowC7 ⋊ C2×C32×C67
HallC3×ΓL(1,𝔽8)×C67 ⋊ C2
HallD7×C67 ⋊ C32
HallC7×C67 ⋊ C2×C32
HallC3×ΓL(1,𝔽8) ⋊ C2×C67
HallD7 ⋊ C32×C67

Subgroups

subgroupG/H
center, hypercenterC3×C67AGL(1,𝔽7)
commutator, hypocenterC7C2×C32×C67
FrattiniC1G
Fitting, socleC3×C7×C67C2×C3
LCSG ▷ C7
UCSC1 ◁ C3×C67

48 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1407 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC3×AGL(1,𝔽7)×D67, D3×AGL(1,𝔽7)×C67, AGL(1,𝔽7)×D201, …
maximal normal subgroup ofC3×AGL(1,𝔽7)×D67, D3×AGL(1,𝔽7)×C67, AGL(1,𝔽7)×D201, …
maximal quotient ofC3×C67×ΓL(1,𝔽8)⋊C4, C2×C3×AGL(1,𝔽7)×C67

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(8442, 31);