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D₄×D₇×C₃⋊D₃ #72245442

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

Aliases

D₄×D₇×C₃⋊D₃

Splittings

Fitting	C₃²×C₇×D₄ ⋊ C₂²
Hall	C₃²×C₇ ⋊ C₂²×D₄
Sylow	C₃² ⋊ C₂×D₄×D₇
Sylow	C₇ ⋊ C₂×D₄×C₃⋊D₃

Subgroups

	subgroup	G/H
center, Frattini	C₂	C₂²×D₇×C₃⋊D₃
commutator, socle, cosocle	C₂×C₃²×C₇	C₂⁴
Fitting	C₃²×C₇×D₄	C₂²
hypercenter	D₄	D₇×C₃⋊D₃
hypocenter	C₃²×C₇	C₂²×D₄
LCS	G ▷ C₂×C₃²×C₇ ▷ C₃²×C₇
UCS	C₁ ◁ C₂ ◁ D₄

1416 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 252

Conjugacy classes & character table

150 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₂×D₄×D₇×C₃⋊D₃, D₄×C₃⋊D₃×AGL(1,𝔽₇), D₇×#63930, …
maximal normal subgroup of	C₂×D₄×D₇×C₃⋊D₃, D₄×C₃⋊D₃×AGL(1,𝔽₇), D₇×#63930, …
maximal quotient of	C₂×D₄×D₇×C₃⋊D₃, C₃⋊D₃×#6503, D₇×#64149, …

GAP

Past the SmallGroups library coverage — no SmallGroups id.