Finite Group Databasebeta

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C₄×#13094713 #72246433

order	6048
automorphism	?
homology	Abelianization (H₁) = C₂×C₃×C₄² · Schur multiplier (H₂) = C₂²×C₃×C₄

Aliases

C₄×#13094713

Splittings

derived	C₃²×C₇ ⋊ C₂×C₃×C₄²
Hall	C₃²×ΓL(1,𝔽₈) ⋊ C₂×C₄²
Sylow	C₇ ⋊ C₃×C₄²×C₃⋊D₃

Subgroups

	subgroup	G/H
center, hypercenter	C₂×C₄	C₃⋊D₃×AGL(1,𝔽₇)
commutator, hypocenter	C₃²×C₇	C₂×C₃×C₄²
Frattini	C₂²	C₂×C₃⋊D₃×AGL(1,𝔽₇)
Fitting	C₂×C₃²×C₄×C₇	C₂²×C₃
socle, cosocle	C₂²×C₃²×C₇	C₂³×C₃
prime radical	C₂²×C₃⋊(C₃⋊AGL(1,𝔽₇))	C₂²
LCS	G ▷ C₃²×C₇
UCS	C₁ ◁ C₂×C₄

1536 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 1008

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₄²×C₃⋊D₃×AGL(1,𝔽₇), #72246558
maximal normal subgroup of	C₄²×C₃⋊D₃×AGL(1,𝔽₇), #72246558

GAP

Past the SmallGroups library coverage — no SmallGroups id.