Finite Group Databasebeta

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D₃×D₄×AGL(1,𝔽₇) #72222055

order	2016
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₃ · Schur multiplier (H₂) = C₂⁶

Aliases

D₃×D₄×AGL(1,𝔽₇)

Splittings

Fitting	C₃×C₇×D₄ ⋊ C₂²×C₃
Hall	C₃×ΓL(1,𝔽₈) ⋊ C₂²×D₄
Sylow	C₇ ⋊ C₂×C₃×D₃×D₄

Subgroups

	subgroup	G/H
center, Frattini	C₂	C₂²×D₃×AGL(1,𝔽₇)
commutator, socle, cosocle	C₂×C₃×C₇	C₂⁴×C₃
Fitting	C₃×C₇×D₄	C₂²×C₃
hypercenter	D₄	D₃×AGL(1,𝔽₇)
hypocenter	C₃×C₇	C₂²×C₃×D₄
LCS	G ▷ C₂×C₃×C₇ ▷ C₃×C₇
UCS	C₁ ◁ C₂ ◁ D₄

998 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

105 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	AGL(1,𝔽₇)×#3811, D₃×#72210376, D₃×S₄×AGL(1,𝔽₇), …
maximal normal subgroup of	C₂×D₃×D₄×AGL(1,𝔽₇), AGL(1,𝔽₇)×#1004, D₃×#6548⋊C₃, …
maximal quotient of	AGL(1,𝔽₇)×#3811, D₃×#72210376, C₂×D₃×D₄×AGL(1,𝔽₇), …
automorphism group of	Dic₄₂, D₈₄, C₂×Dic₂₁
holomorph of	C₃×C₄×C₇

GAP

Past the SmallGroups library coverage — no SmallGroups id.