Finite Group Databasebeta

← Prev (#21439733) Next (#21439735) →

C2×C13×D7×ΓL(1,𝔽8) #21439734

order7644
automorphism?
homologyAbelianization (H1) = C22×C3×C13 · Schur multiplier (H2) = C2

Aliases

direct productC2×C13×D7×ΓL(1,𝔽8)

Splittings

Fitting, socleC2×C72×C13 ⋊ C2×C3
derived, SylowC72 ⋊ C22×C3×C13
HallC2×C7×C13×D7 ⋊ C3
HallC7×C13×ΓL(1,𝔽8) ⋊ C22
HallC72×C13 ⋊ C22×C3
HallC2×C7×D7 ⋊ C3×C13
HallC7×ΓL(1,𝔽8) ⋊ C22×C13

Subgroups

subgroupG/H
center, hypercenterC2×C13D7×ΓL(1,𝔽8)
commutator, hypocenterC72C22×C3×C13
FrattiniC1G
Fitting, socleC2×C72×C13C2×C3
LCSG ▷ C72
UCSC1 ◁ C2×C13

84 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

650 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC2×C13×ΓL(1,𝔽8)×AGL(1,𝔽7), C2×ΓL(1,𝔽8)×#10587721, C2×ΓL(1,𝔽8)×#10587720, …
maximal normal subgroup ofC2×C13×ΓL(1,𝔽8)×AGL(1,𝔽7), C2×ΓL(1,𝔽8)×#10587721, C2×ΓL(1,𝔽8)×#10587720, …
maximal quotient ofC2×C13×D7×C7⋊C9, D3×C13×D7×ΓL(1,𝔽8), C2×C3×C13×D7×ΓL(1,𝔽8), …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(7644, 303);