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AGL(1,𝔽7)×C11⋊C25 #26040471

order11550
automorphism?
homologyAbelianization (H1) = C2×C3×C25 · Schur multiplier (H2) = C1

Aliases

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

Splittings

derived, HallC7×C11 ⋊ C2×C3×C25
HallΓL(1,𝔽8)×C11⋊C25 ⋊ C2
HallD7×C11⋊C25 ⋊ C3
HallC7×C11⋊C25 ⋊ C2×C3
HallC11×AGL(1,𝔽7) ⋊ C25
HallC11×ΓL(1,𝔽8) ⋊ C2×C25
HallC11×D7 ⋊ C3×C25
HallΓL(1,𝔽8) ⋊ C2×C11⋊C25
HallD7 ⋊ C3×C11⋊C25
SylowC11 ⋊ C25×AGL(1,𝔽7)
SylowC7 ⋊ C2×C3×C11⋊C25

Subgroups

subgroupG/H
center, Frattini, hypercenterC5AGL(1,𝔽7)×C11⋊C5
commutator, hypocenterC7×C11C2×C3×C25
Fitting, socle, cosocleC5×C7×C11C2×C3×C5
prime radicalC5×C11×AGL(1,𝔽7)C5
LCSG ▷ C7×C11
UCSC1 ◁ C5

48 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

245 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofAGL(1,𝔽7)×D11⋊C25, C2×AGL(1,𝔽7)×C11⋊C25, C3×AGL(1,𝔽7)×C11⋊C25, …
maximal normal subgroup ofAGL(1,𝔽7)×D11⋊C25, C2×AGL(1,𝔽7)×C11⋊C25, C3×AGL(1,𝔽7)×C11⋊C25
maximal quotient ofΓL(1,𝔽8)⋊C4×C11⋊C25, C2×AGL(1,𝔽7)×C11⋊C25, D7⋊C9×C11⋊C25, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11550, 35);