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D₇×ΓL(1,𝔽₈)×D₁₃ #21439663

order	7644
automorphism	?
homology	Abelianization (H₁) = C₂²×C₃ · Schur multiplier (H₂) = C₂

Aliases

D₇×ΓL(1,𝔽₈)×D₁₃

Splittings

Fitting, socle, derived, Hall	C₇²×C₁₃ ⋊ C₂²×C₃
Hall	C₇×D₇×D₁₃ ⋊ C₃
Hall	C₇×C₁₃×ΓL(1,𝔽₈) ⋊ C₂²
Hall	C₇×ΓL(1,𝔽₈) ⋊ C₂×D₁₃
Sylow	C₇² ⋊ C₂×C₃×D₁₃
Sylow	C₁₃ ⋊ C₂×D₇×ΓL(1,𝔽₈)

Subgroups

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, hypocenter	C₇²×C₁₃	C₂²×C₃
LCS	G ▷ C₇²×C₁₃
UCS	C₁

84 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

200 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	ΓL(1,𝔽₈)×#10587716⋊C₂, ΓL(1,𝔽₈)×#10587717⋊C₂, ΓL(1,𝔽₈)×D₁₃×AGL(1,𝔽₇), …
maximal normal subgroup of	ΓL(1,𝔽₈)×#10587716⋊C₂, ΓL(1,𝔽₈)×#10587717⋊C₂, ΓL(1,𝔽₈)×D₁₃×AGL(1,𝔽₇), …
maximal quotient of	D₇×D₁₃×C₇⋊C₉, C₃×D₇×ΓL(1,𝔽₈)×D₁₃, ΓL(1,𝔽₈)×D₁₃×D₂₁, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(7644, 232);