Finite Group Databasebeta

← Prev (#26039570) Next (#26039572) →

C2×C13×ΓL(1,𝔽8)2 #26039571

order11466
automorphism?
homologyAbelianization (H1) = C2×C32×C13 · Schur multiplier (H2) = C3

Aliases

direct productC2×C13×ΓL(1,𝔽8)2
unambiguous semidirect product(C2×C7×ΓL(1,𝔽8))⋊(C3×C13)
unambiguous semidirect product(C2×#3861)⋊(C3×C13)
unambiguous semidirect product(C2×#3862)⋊(C3×C13)

Splittings

Fitting, socle, HallC2×C72×C13 ⋊ C32
derived, SylowC72 ⋊ C2×C32×C13
HallC72×C13 ⋊ C2×C32
HallC2×C72 ⋊ C32×C13

Subgroups

subgroupG/H
center, hypercenterC2×C13ΓL(1,𝔽8)2
commutator, cosocle, hypocenterC72C2×C32×C13
FrattiniC1G
Fitting, socleC2×C72×C13C32
LCSG ▷ C72
UCSC1 ◁ C2×C13

112 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

650 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC13×ΓL(1,𝔽8)⋊(ΓL(1,𝔽8)⋊C4), ΓL(1,𝔽8)⋊(ΓL(1,𝔽8)⋊Dic13), C13×ΓL(1,𝔽8)×ΓL(1,𝔽8)⋊C4, …
maximal normal subgroup ofC13×ΓL(1,𝔽8)⋊(ΓL(1,𝔽8)⋊C4), ΓL(1,𝔽8)⋊(ΓL(1,𝔽8)⋊Dic13), C13×ΓL(1,𝔽8)×ΓL(1,𝔽8)⋊C4, …
maximal quotient ofC4×C13×ΓL(1,𝔽8)2, C22×C13×ΓL(1,𝔽8)2

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11466, 214);