Finite Group Databasebeta

← Prev (#26040462) Next (#26040464) →

ΓL(1,𝔽8)×D11×C25 #26040463

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

Aliases

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

Splittings

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

Subgroups

subgroupG/H
center, hypercenterC25ΓL(1,𝔽8)×D11
commutator, hypocenterC7×C11C2×C3×C25
FrattiniC5C5×ΓL(1,𝔽8)×D11
FittingC7×C11×C25C2×C3
socle, cosocleC5×C7×C11C2×C3×C5
prime radicalC5×ΓL(1,𝔽8)×D11C5
LCSG ▷ C7×C11
UCSC1 ◁ C25

48 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

875 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofD11×C25×AGL(1,𝔽7), D11×ΓL(1,𝔽8)⋊D25, ΓL(1,𝔽8)×D11×D25, …
maximal normal subgroup ofD11×C25×AGL(1,𝔽7), D11×ΓL(1,𝔽8)⋊D25, ΓL(1,𝔽8)×D11×D25, …
maximal quotient ofΓL(1,𝔽8)×C25×Dic11, C2×ΓL(1,𝔽8)×D11×C25, D11×C25×C7⋊C9, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11550, 27);