Finite Group Databasebeta

← Prev (#30633527) Next (#30633529) →

C5×C7×ΓL(1,𝔽8)×D11 #30633528

order16170
automorphism?
homologyAbelianization (H1) = C2×C3×C5×C7 · Schur multiplier (H2) = C1

Aliases

direct productC5×C7×ΓL(1,𝔽8)×D11
unambiguous semidirect product(C5×C7×D11)⋊(C3×C7)

Splittings

Fitting, socle, HallC5×C72×C11 ⋊ C2×C3
derivedC7×C11 ⋊ C2×C3×C5×C7
HallC5×C7×C11×ΓL(1,𝔽8) ⋊ C2
HallC5×C72×D11 ⋊ C3
HallC7×C11×ΓL(1,𝔽8) ⋊ C2×C5
HallC72×D11 ⋊ C3×C5
HallC72×C11 ⋊ C2×C3×C5
HallC5×C72 ⋊ C3×D11
HallC5×C11 ⋊ C2×C7×ΓL(1,𝔽8)
SylowC72 ⋊ C3×C5×D11
SylowC11 ⋊ C2×C5×C7×ΓL(1,𝔽8)

Subgroups

subgroupG/H
center, hypercenterC5×C7ΓL(1,𝔽8)×D11
commutator, cosocle, hypocenterC7×C11C2×C3×C5×C7
FrattiniC1G
Fitting, socleC5×C72×C11C2×C3
LCSG ▷ C7×C11
UCSC1 ◁ C5×C7

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1155

Conjugacy classes & character table

1225 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC5×C7×D11×AGL(1,𝔽7), C5×D11×ΓL(1,𝔽8)⋊D7, C5×D7×ΓL(1,𝔽8)×D11, …
maximal normal subgroup ofC5×C7×D11×AGL(1,𝔽7), C5×D11×ΓL(1,𝔽8)⋊D7, C5×D7×ΓL(1,𝔽8)×D11, …
maximal quotient ofC5×C7×ΓL(1,𝔽8)×Dic11, C2×C5×C7×ΓL(1,𝔽8)×D11

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(16170, 73);