Finite Group Databasebeta

← Prev (#72246426) Next (#72246428) →

C₃²×C₄²×AGL(1,𝔽₇) #72246427

order	6048
automorphism	?
homology	Abelianization (H₁) = C₂×C₃³×C₄² · Schur multiplier (H₂) = C₂²×C₃³×C₄

Aliases

C₃²×C₄²×AGL(1,𝔽₇)

Splittings

Fitting	C₃²×C₄²×C₇ ⋊ C₂×C₃
derived, Sylow	C₇ ⋊ C₂×C₃³×C₄²
Hall	C₄²×D₇ ⋊ C₃³
Hall	C₃²×ΓL(1,𝔽₈) ⋊ C₂×C₄²

Subgroups

	subgroup	G/H
center, hypercenter	C₃²×C₄²	AGL(1,𝔽₇)
commutator, hypocenter	C₇	C₂×C₃³×C₄²
Frattini	C₂²	C₂²×C₃²×AGL(1,𝔽₇)
Fitting	C₃²×C₄²×C₇	C₂×C₃
socle	C₂²×C₃²×C₇	C₂³×C₃
prime radical	C₂²×C₃²×AGL(1,𝔽₇)	C₂²
cosocle	C₂²×C₇	C₂³×C₃³
LCS	G ▷ C₇
UCS	C₁ ◁ C₃²×C₄²

3024 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 1008

Conjugacy classes & character table

1008 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₄²×C₃⋊D₃×AGL(1,𝔽₇), C₃²×#127×AGL(1,𝔽₇), AGL(1,𝔽₇)×#64083
maximal normal subgroup of	C₄²×C₃⋊D₃×AGL(1,𝔽₇), C₃²×#127×AGL(1,𝔽₇), AGL(1,𝔽₇)×#64083

GAP

Past the SmallGroups library coverage — no SmallGroups id.