Finite Group Databasebeta

← Prev (#13132953) Next (#13132955) →

C23×C5⋊AGL(1,𝔽7) #13132954

order1680
isoclinismisoclinic class of C5⋊AGL(1,𝔽7)
automorphism?
homologyAbelianization (H1) = C24×C3 · Schur multiplier (H2) = C26

Aliases

direct productC23×C5⋊AGL(1,𝔽7)

Splittings

Fitting, socleC23×C5×C7 ⋊ C2×C3
derived, HallC5×C7 ⋊ C24×C3
HallC23×D35 ⋊ C3
HallC5×ΓL(1,𝔽8) ⋊ C24
HallΓL(1,𝔽8) ⋊ C23×D5
SylowC7 ⋊ C23×C3×D5
SylowC5 ⋊ C23×AGL(1,𝔽7)

Subgroups

subgroupG/H
center, hypercenterC23C5⋊AGL(1,𝔽7)
commutator, cosocle, hypocenterC5×C7C24×C3
FrattiniC1G
Fitting, socleC23×C5×C7C2×C3
LCSG ▷ C5×C7
UCSC1 ◁ C23

536 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 280

Conjugacy classes & character table

136 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC23×D5×AGL(1,𝔽7), C2×D4×C5⋊AGL(1,𝔽7), C2×#10587963⋊C3, …
maximal normal subgroup ofC23×D5×AGL(1,𝔽7), C2×D4×C5⋊AGL(1,𝔽7), C2×#10587963⋊C3, …
maximal quotient ofC2×D4×C5⋊AGL(1,𝔽7), C24×C5⋊AGL(1,𝔽7), #41×C5⋊AGL(1,𝔽7)

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1680, 974);