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C73×AGL(1,𝔽11) #22548566

order8030
isoclinismisoclinic class of AGL(1,𝔽11)
automorphism?
homologyAbelianization (H1) = C2×C5×C73 · Schur multiplier (H2) = C1

Aliases

direct productC73×AGL(1,𝔽11)
unambiguous semidirect productD11⋊(C5×C73)
unambiguous semidirect product(C11⋊C5)⋊(C2×C73)
unambiguous semidirect product(D11×C73)⋊C5

Splittings

Fitting, socle, HallC11×C73 ⋊ C2×C5
derived, SylowC11 ⋊ C2×C5×C73
HallC11⋊C5×C73 ⋊ C2
HallD11×C73 ⋊ C5
HallC11⋊C5 ⋊ C2×C73
HallD11 ⋊ C5×C73

Subgroups

subgroupG/H
center, hypercenterC73AGL(1,𝔽11)
commutator, hypocenterC11C2×C5×C73
FrattiniC1G
Fitting, socleC11×C73C2×C5
LCSG ▷ C11
UCSC1 ◁ C73

16 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

803 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofAGL(1,𝔽11)×D73, C2×C73×AGL(1,𝔽11), C3×C73×AGL(1,𝔽11), …
maximal normal subgroup ofAGL(1,𝔽11)×D73, C2×C73×AGL(1,𝔽11), C3×C73×AGL(1,𝔽11), …
maximal quotient ofC73×Dic11⋊C5, C2×C73×AGL(1,𝔽11), C3×C73×AGL(1,𝔽11), …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(8030, 11);