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D₇×ΓL(1,𝔽₈)×C₂₉ #22555347

order	8526
automorphism	?
homology	Abelianization (H₁) = C₂×C₃×C₂₉ · Schur multiplier (H₂) = C₁

Aliases

D₇×ΓL(1,𝔽₈)×C₂₉

Splittings

Fitting, socle, Hall	C₇²×C₂₉ ⋊ C₂×C₃
derived, Sylow	C₇² ⋊ C₂×C₃×C₂₉
Hall	C₇×ΓL(1,𝔽₈)×C₂₉ ⋊ C₂
Hall	C₇×D₇×C₂₉ ⋊ C₃
Hall	C₇×ΓL(1,𝔽₈) ⋊ C₂×C₂₉
Hall	C₇×D₇ ⋊ C₃×C₂₉

Subgroups

	subgroup	G/H
center, hypercenter	C₂₉	D₇×ΓL(1,𝔽₈)
commutator, hypocenter	C₇²	C₂×C₃×C₂₉
Frattini	C₁	G
Fitting, socle	C₇²×C₂₉	C₂×C₃
LCS	G ▷ C₇²
UCS	C₁ ◁ C₂₉

34 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

725 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	D₇×C₂₉×AGL(1,𝔽₇), D₇×ΓL(1,𝔽₈)⋊D₂₉, D₇×ΓL(1,𝔽₈)×D₂₉, …
maximal normal subgroup of	D₇×C₂₉×AGL(1,𝔽₇), D₇×ΓL(1,𝔽₈)⋊D₂₉, D₇×ΓL(1,𝔽₈)×D₂₉, …
maximal quotient of	ΓL(1,𝔽₈)×Dic₇×C₂₉, C₂×D₇×ΓL(1,𝔽₈)×C₂₉, D₇×C₂₉×C₇⋊C₉, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(8526, 45);