Finite Group Databasebeta

← Prev (#22604117) Next (#22604119) →

C3×AGL(1,𝔽7)×C73 #22604118

order9198
isoclinismisoclinic class of AGL(1,𝔽7)
automorphism?
homologyAbelianization (H1) = C2×C32×C73 · Schur multiplier (H2) = C3

Aliases

direct productC3×AGL(1,𝔽7)×C73
unambiguous semidirect productD7⋊(C32×C73)
unambiguous semidirect productΓL(1,𝔽8)⋊(C2×C3×C73)
unambiguous semidirect product(C3×D7)⋊(C3×C73)

Splittings

Fitting, socleC3×C7×C73 ⋊ C2×C3
derived, SylowC7 ⋊ C2×C32×C73
HallC3×ΓL(1,𝔽8)×C73 ⋊ C2
HallD7×C73 ⋊ C32
HallC7×C73 ⋊ C2×C32
HallC3×ΓL(1,𝔽8) ⋊ C2×C73
HallD7 ⋊ C32×C73

Subgroups

subgroupG/H
center, hypercenterC3×C73AGL(1,𝔽7)
commutator, hypocenterC7C2×C32×C73
FrattiniC1G
Fitting, socleC3×C7×C73C2×C3
LCSG ▷ C7
UCSC1 ◁ C3×C73

48 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1533 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC3×AGL(1,𝔽7)×D73, D3×AGL(1,𝔽7)×C73, AGL(1,𝔽7)×D219, …
maximal normal subgroup ofC3×AGL(1,𝔽7)×D73, D3×AGL(1,𝔽7)×C73, AGL(1,𝔽7)×D219, …
maximal quotient ofC3×C73×ΓL(1,𝔽8)⋊C4, C2×C3×AGL(1,𝔽7)×C73

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(9198, 43);