Finite Group Databasebeta

← Prev (#20301226) Next (#20301228) →

D₇×ΓL(1,𝔽₈)×C₂₅ #20301227

order	7350
automorphism	?
homology	Abelianization (H₁) = C₂×C₃×C₂₅ · Schur multiplier (H₂) = C₁

Aliases

D₇×ΓL(1,𝔽₈)×C₂₅

Splittings

Fitting, Hall	C₇²×C₂₅ ⋊ C₂×C₃
derived, Sylow	C₇² ⋊ C₂×C₃×C₂₅
Hall	C₇×ΓL(1,𝔽₈)×C₂₅ ⋊ C₂
Hall	C₇×D₇×C₂₅ ⋊ C₃
Hall	C₇×ΓL(1,𝔽₈) ⋊ C₂×C₂₅
Hall	C₇×D₇ ⋊ C₃×C₂₅

Subgroups

	subgroup	G/H
center, hypercenter	C₂₅	D₇×ΓL(1,𝔽₈)
commutator, hypocenter	C₇²	C₂×C₃×C₂₅
Frattini	C₅	C₅×D₇×ΓL(1,𝔽₈)
Fitting	C₇²×C₂₅	C₂×C₃
socle	C₅×C₇²	C₂×C₃×C₅
LCS	G ▷ C₇²
UCS	C₁ ◁ C₂₅

51 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

625 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	D₇×C₂₅×AGL(1,𝔽₇), D₇×ΓL(1,𝔽₈)⋊D₂₅, D₇×ΓL(1,𝔽₈)×D₂₅, …
maximal normal subgroup of	D₇×C₂₅×AGL(1,𝔽₇), D₇×ΓL(1,𝔽₈)⋊D₂₅, D₇×ΓL(1,𝔽₈)×D₂₅, …
maximal quotient of	ΓL(1,𝔽₈)×C₂₅×Dic₇, C₂×D₇×ΓL(1,𝔽₈)×C₂₅, D₇×C₂₅×C₇⋊C₉, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(7350, 50);