Finite Group Databasebeta

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C₂×C₃²×D₄×D₇ #72245449

order	2016
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₃² · Schur multiplier (H₂) = C₂⁶×C₃

Aliases

C₂×C₃²×D₄×D₇

Splittings

Fitting	C₂×C₃²×C₇×D₄ ⋊ C₂
Hall	C₃²×C₇ ⋊ C₂²×D₄
Sylow	C₇ ⋊ C₂²×C₃²×D₄

Subgroups

1416 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 504

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₂×D₄×D₇×C₃⋊D₃, C₂×C₃²×D₄×AGL(1,𝔽₇), C₃×D₇×#932, …
maximal normal subgroup of	C₂×D₄×D₇×C₃⋊D₃, C₂×C₃²×D₄×AGL(1,𝔽₇), C₃×D₇×#932, …
maximal quotient of	C₃²×D₇×#127, C₃²×D₇×#120

GAP

Past the SmallGroups library coverage — no SmallGroups id.