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ΓL(1,𝔽8)×D275 #26040467

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

Aliases

direct productΓL(1,𝔽8)×D275
unambiguous semidirect productC11⋊(ΓL(1,𝔽8)×D25)
unambiguous semidirect productC25⋊(ΓL(1,𝔽8)×D11)
unambiguous semidirect product(C7×D275)⋊C3

Splittings

Fitting, derived, HallC7×C11×C25 ⋊ C2×C3
HallC11×ΓL(1,𝔽8)×C25 ⋊ C2
HallC7×D275 ⋊ C3
HallΓL(1,𝔽8)×C25 ⋊ D11
HallC11×C25 ⋊ C2×ΓL(1,𝔽8)
HallC11×ΓL(1,𝔽8) ⋊ D25
HallC7×C25 ⋊ C3×D11
HallC7×C11 ⋊ C3×D25
SylowC25 ⋊ ΓL(1,𝔽8)×D11
SylowC11 ⋊ ΓL(1,𝔽8)×D25
SylowC7 ⋊ C3×D275

Subgroups

subgroupG/H
center, hypercenterC1G
commutator, Fitting, cosocle, hypocenterC7×C11×C25C2×C3
FrattiniC5ΓL(1,𝔽8)×D55
socleC5×C7×C11C3×D5
LCSG ▷ C7×C11×C25
UCSC1

48 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

695 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofAGL(1,𝔽7)×D275, (C11⋊AGL(1,𝔽7))⋊D25, ΓL(1,𝔽8)×D11×D25, …
maximal normal subgroup ofAGL(1,𝔽7)×D275, (C11⋊AGL(1,𝔽7))⋊D25, ΓL(1,𝔽8)×D11×D25, …
maximal quotient ofΓL(1,𝔽8)×Dic275, C2×ΓL(1,𝔽8)×D275, C7⋊C9×D275, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11550, 31);