Finite Group Databasebeta

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D₃×#127×AGL(1,𝔽₇) #72244277

order	8064
automorphism	?
homology	Abelianization (H₁) = C₂⁵×C₃ · Schur multiplier (H₂) = C₂⁹×C₄

Aliases

D₃×#127×AGL(1,𝔽₇)

Splittings

Fitting	C₃×C₇×#127 ⋊ C₂²×C₃
Hall	C₃×ΓL(1,𝔽₈) ⋊ C₂²×#127
Sylow	C₇ ⋊ C₂×C₃×D₃×#127

Subgroups

	subgroup	G/H
center, Frattini	C₂²	C₂³×D₃×AGL(1,𝔽₇)
commutator, socle, cosocle	C₂²×C₃×C₇	C₂⁵×C₃
Fitting	C₃×C₇×#127	C₂²×C₃
hypercenter	#127	D₃×AGL(1,𝔽₇)
hypocenter	C₃×C₇	C₂²×C₃×#127
LCS	G ▷ C₂²×C₃×C₇ ▷ C₃×C₇
UCS	C₁ ◁ C₂² ◁ #127

12498 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 336

Conjugacy classes & character table

294 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₃⋊D₃×#127×AGL(1,𝔽₇), D₃×AGL(1,𝔽₇)×#453
maximal normal subgroup of	D₃×AGL(1,𝔽₇)×#453
maximal quotient of	C₃⋊D₃×#127×AGL(1,𝔽₇)

GAP

Past the SmallGroups library coverage — no SmallGroups id.