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C₂×C₃⋊D₃×C₄⋊AGL(1,𝔽₇) #72245599

order	6048
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₃ · Schur multiplier (H₂) = C₂⁶×C₃

Aliases

C₂×C₃⋊D₃×C₄⋊AGL(1,𝔽₇)

Splittings

Fitting	C₂×C₃²×C₄×C₇ ⋊ C₂²×C₃
Hall	C₃²×ΓL(1,𝔽₈) ⋊ C₂²×D₄
Sylow	C₇ ⋊ C₂×C₃×D₄×C₃⋊D₃

Subgroups

3264 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 504

Conjugacy classes & character table

228 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₂×D₄×C₃⋊D₃×AGL(1,𝔽₇), C₃⋊D₃×#10620710, C₃⋊D₃×#6503⋊C₃, …
maximal normal subgroup of	C₂×D₄×C₃⋊D₃×AGL(1,𝔽₇), C₃⋊D₃×#10620710, C₃⋊D₃×#6503⋊C₃, …
maximal quotient of	C₃⋊D₃×#10620710, C₃⋊D₃×#6445⋊C₃

GAP

Past the SmallGroups library coverage — no SmallGroups id.