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C11×C25×AGL(1,𝔽7) #26040464

order11550
isoclinismisoclinic class of AGL(1,𝔽7)
automorphism?
homologyAbelianization (H1) = C2×C3×C11×C25 · Schur multiplier (H2) = C1

Aliases

direct productC11×C25×AGL(1,𝔽7)
unambiguous semidirect productD7⋊(C3×C11×C25)
unambiguous semidirect productΓL(1,𝔽8)⋊(C2×C11×C25)
unambiguous semidirect product(D7×C25)⋊(C3×C11)
unambiguous semidirect product(C11×D7×C25)⋊C3

Splittings

Fitting, HallC7×C11×C25 ⋊ C2×C3
derived, SylowC7 ⋊ C2×C3×C11×C25
HallC11×ΓL(1,𝔽8)×C25 ⋊ C2
HallC11×D7×C25 ⋊ C3
HallΓL(1,𝔽8)×C25 ⋊ C2×C11
HallD7×C25 ⋊ C3×C11
HallC11×ΓL(1,𝔽8) ⋊ C2×C25
HallC7×C25 ⋊ C2×C3×C11
HallC11×D7 ⋊ C3×C25
HallC7×C11 ⋊ C2×C3×C25
HallΓL(1,𝔽8) ⋊ C2×C11×C25
HallD7 ⋊ C3×C11×C25

Subgroups

subgroupG/H
center, hypercenterC11×C25AGL(1,𝔽7)
commutator, hypocenterC7C2×C3×C11×C25
FrattiniC5C5×C11×AGL(1,𝔽7)
FittingC7×C11×C25C2×C3
socleC5×C7×C11C2×C3×C5
prime radicalC5×C11×AGL(1,𝔽7)C5
cosocleC5×C7C2×C3×C5×C11
LCSG ▷ C7
UCSC1 ◁ C11×C25

48 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1925 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofD11×C25×AGL(1,𝔽7), C11×AGL(1,𝔽7)×D25, AGL(1,𝔽7)×D275, …
maximal normal subgroup ofD11×C25×AGL(1,𝔽7), C11×AGL(1,𝔽7)×D25, AGL(1,𝔽7)×D275, …
maximal quotient ofC11×C25×ΓL(1,𝔽8)⋊C4, C2×C11×C25×AGL(1,𝔽7), C11×C25×D7⋊C9, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11550, 28);