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C₄²×D₃×AGL(1,𝔽₇) #72244261

order	4032
automorphism	?
homology	Abelianization (H₁) = C₂²×C₃×C₄² · Schur multiplier (H₂) = C₂⁵×C₄

Aliases

C₄²×D₃×AGL(1,𝔽₇)

Splittings

Fitting	C₃×C₄²×C₇ ⋊ C₂²×C₃
derived	C₃×C₇ ⋊ C₂²×C₃×C₄²
Hall	C₃×ΓL(1,𝔽₈) ⋊ C₂²×C₄²
Sylow	C₇ ⋊ C₂×C₃×C₄²×D₃

Subgroups

	subgroup	G/H
center, hypercenter	C₄²	D₃×AGL(1,𝔽₇)
commutator, hypocenter	C₃×C₇	C₂²×C₃×C₄²
Frattini	C₂²	C₂²×D₃×AGL(1,𝔽₇)
Fitting	C₃×C₄²×C₇	C₂²×C₃
socle, cosocle	C₂²×C₃×C₇	C₂⁴×C₃
prime radical	C₂²×D₃×AGL(1,𝔽₇)	C₂²
LCS	G ▷ C₃×C₇
UCS	C₁ ◁ C₄²

2100 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 336

Conjugacy classes & character table

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

Relationships

maximal subgroup of	D₃×#127×AGL(1,𝔽₇), C₄²×C₃⋊D₃×AGL(1,𝔽₇), D₃×#104×AGL(1,𝔽₇)
maximal normal subgroup of	D₃×#127×AGL(1,𝔽₇), D₃×#104×AGL(1,𝔽₇)
maximal quotient of	C₄²×C₃⋊D₃×AGL(1,𝔽₇)

GAP

Past the SmallGroups library coverage — no SmallGroups id.