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ΓL(1,𝔽8)×D11⋊C25 #26040470

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

Aliases

direct productΓL(1,𝔽8)×D11⋊C25
unambiguous semidirect productD11⋊(ΓL(1,𝔽8)×C25)
unambiguous semidirect product(C11⋊C25)⋊(C2×ΓL(1,𝔽8))
unambiguous semidirect product(ΓL(1,𝔽8)×D11)⋊C25
unambiguous semidirect product(C7×D11⋊C25)⋊C3

Splittings

derived, HallC7×C11 ⋊ C2×C3×C25
HallΓL(1,𝔽8)×C11⋊C25 ⋊ C2
HallC7×D11⋊C25 ⋊ C3
HallC7×C11⋊C25 ⋊ C2×C3
HallΓL(1,𝔽8)×D11 ⋊ C25
HallC11⋊C25 ⋊ C2×ΓL(1,𝔽8)
HallC11×ΓL(1,𝔽8) ⋊ C2×C25
HallC7×D11 ⋊ C3×C25
HallD11 ⋊ ΓL(1,𝔽8)×C25
SylowC11 ⋊ C2×ΓL(1,𝔽8)×C25
SylowC7 ⋊ C3×D11⋊C25

Subgroups

subgroupG/H
center, Frattini, hypercenterC5ΓL(1,𝔽8)×AGL(1,𝔽11)
commutator, hypocenterC7×C11C2×C3×C25
Fitting, socle, cosocleC5×C7×C11C2×C3×C5
prime radicalC5×ΓL(1,𝔽8)×D11C5
LCSG ▷ C7×C11
UCSC1 ◁ C5

48 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

275 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofAGL(1,𝔽7)×D11⋊C25, C2×ΓL(1,𝔽8)×D11⋊C25, C3×ΓL(1,𝔽8)×D11⋊C25, …
maximal normal subgroup ofAGL(1,𝔽7)×D11⋊C25, C2×ΓL(1,𝔽8)×D11⋊C25, C3×ΓL(1,𝔽8)×D11⋊C25
maximal quotient ofΓL(1,𝔽8)×Dic11⋊C25, C2×ΓL(1,𝔽8)×D11⋊C25, C7⋊C9×D11⋊C25, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11550, 34);