Finite Group Databasebeta

← Prev (#72218363) Next (#72218365) →

C5×#41×AGL(1,𝔽7) #72218364

order3360
automorphism?
homologyAbelianization (H1) = C24×C3×C5 · Schur multiplier (H2) = C25

Aliases

direct productC5×#41×AGL(1,𝔽7)

Splittings

FittingC5×C7×#41 ⋊ C2×C3
HallC5×D7×#41 ⋊ C3
HallD7×#41 ⋊ C3×C5
HallC5×ΓL(1,𝔽8) ⋊ C2×#41
HallC5×C7 ⋊ C2×C3×#41
HallΓL(1,𝔽8) ⋊ C2×C5×#41
SylowC7 ⋊ C2×C3×C5×#41

Subgroups

subgroupG/H
centerC4×C5C22×AGL(1,𝔽7)
commutator, cosocleC2×C7C24×C3×C5
FrattiniC2C23×C5×AGL(1,𝔽7)
FittingC5×C7×#41C2×C3
socleC2×C5×C7C24×C3
hypercenterC5×#41AGL(1,𝔽7)
hypocenterC7C2×C3×C5×#41
LCSG ▷ C2×C7 ▷ C7
UCSC1 ◁ C4×C5 ◁ C5×#41

656 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

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

Relationships

maximal subgroup ofD5×#41×AGL(1,𝔽7), C5×AGL(1,ℤ/8)×AGL(1,𝔽7), AGL(1,𝔽7)×#4095
maximal normal subgroup ofD5×#41×AGL(1,𝔽7), C5×AGL(1,ℤ/8)×AGL(1,𝔽7), AGL(1,𝔽7)×#4095

GAP

Past the SmallGroups library coverage — no SmallGroups id.