Finite Group Databasebeta

← Prev (#21440405) Next (#21440407) →

C2×C5×C7⋊AGL(1,𝔽11) #21440406

order7700
automorphism?
homologyAbelianization (H1) = C22×C52 · Schur multiplier (H2) = C2×C5

Aliases

direct productC2×C5×C7⋊AGL(1,𝔽11)
unambiguous semidirect product(C2×C7)⋊(C5×AGL(1,𝔽11))
unambiguous semidirect product(C2×C11⋊C5)⋊(C5×D7)
unambiguous semidirect product(C2×D77)⋊C52
unambiguous semidirect product(C2×C5×D77)⋊C5

Splittings

Fitting, socleC2×C5×C7×C11 ⋊ C2×C5
derived, HallC7×C11 ⋊ C22×C52
HallC5×C7×C11⋊C5 ⋊ C22
HallC2×D77 ⋊ C52
HallC5×C11⋊C5 ⋊ C2×D7
SylowC11 ⋊ C2×C52×D7
SylowC7 ⋊ C2×C5×AGL(1,𝔽11)

Subgroups

subgroupG/H
center, hypercenterC2×C5C7⋊AGL(1,𝔽11)
commutator, hypocenterC7×C11C22×C52
FrattiniC1G
Fitting, socleC2×C5×C7×C11C2×C5
LCSG ▷ C7×C11
UCSC1 ◁ C2×C5

160 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

320 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC2×C5×ΓL(1,𝔽8)⋊AGL(1,𝔽11), C5×D3×C7⋊AGL(1,𝔽11), C2×C3×C5×C7⋊AGL(1,𝔽11), …
maximal normal subgroup ofC2×C5×ΓL(1,𝔽8)⋊AGL(1,𝔽11), C2×C3×C5×C7⋊AGL(1,𝔽11)
maximal quotient ofC5×D3×C7⋊AGL(1,𝔽11), C2×C3×C5×C7⋊AGL(1,𝔽11), C2×C5×C3⋊(C7⋊AGL(1,𝔽11))

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(7700, 70);