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C7×C7⋊AGL(1,𝔽11) #19129128

order5390
automorphism?
homologyAbelianization (H1) = C2×C5×C7 · Schur multiplier (H2) = C1

Aliases

direct productC7×C7⋊AGL(1,𝔽11)
unambiguous semidirect productC7⋊(C7×AGL(1,𝔽11))
unambiguous semidirect product(C11⋊C5)⋊(C7×D7)
unambiguous semidirect productD77⋊(C5×C7)
unambiguous semidirect product(C7×D77)⋊C5

Splittings

Fitting, socle, HallC72×C11 ⋊ C2×C5
derivedC7×C11 ⋊ C2×C5×C7
HallC72×C11⋊C5 ⋊ C2
HallC7×D77 ⋊ C5
HallC11⋊C5 ⋊ C7×D7
SylowC72 ⋊ AGL(1,𝔽11)
SylowC11 ⋊ C5×C7×D7

Subgroups

subgroupG/H
center, hypercenterC7C7⋊AGL(1,𝔽11)
commutator, hypocenterC7×C11C2×C5×C7
FrattiniC1G
Fitting, socleC72×C11C2×C5
LCSG ▷ C7×C11
UCSC1 ◁ C7

44 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

224 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC7×ΓL(1,𝔽8)⋊AGL(1,𝔽11), (C11⋊C5)⋊#64423, (C11⋊C5)⋊#64422, …
maximal normal subgroup ofC7×ΓL(1,𝔽8)⋊AGL(1,𝔽11), (C11⋊C5)⋊#64423, (C11⋊C5)⋊#64422, …
maximal quotient ofC3×C7×C7⋊AGL(1,𝔽11), C7×C3⋊(C7⋊AGL(1,𝔽11)), C7×C7⋊(D11⋊C25), …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(5390, 15);