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D₃×C₈×AGL(1,𝔽₇) #72244556

order	2016
automorphism	?
homology	Abelianization (H₁) = C₂²×C₃×C₈ · Schur multiplier (H₂) = C₂³

Aliases

D₃×C₈×AGL(1,𝔽₇)

Splittings

Fitting	C₃×C₇×C₈ ⋊ C₂²×C₃
derived	C₃×C₇ ⋊ C₂²×C₃×C₈
Hall	C₃×ΓL(1,𝔽₈) ⋊ C₂²×C₈
Sylow	C₇ ⋊ C₂×C₃×D₃×C₈

Subgroups

	subgroup	G/H
center, hypercenter	C₈	D₃×AGL(1,𝔽₇)
commutator, hypocenter	C₃×C₇	C₂²×C₃×C₈
Frattini	C₄	C₂×D₃×AGL(1,𝔽₇)
Fitting	C₃×C₇×C₈	C₂²×C₃
socle	C₂×C₃×C₇	C₂²×C₃×C₄
prime radical	C₂×D₃×AGL(1,𝔽₇)	C₄
cosocle	C₃×C₄×C₇	C₂³×C₃
LCS	G ▷ C₃×C₇
UCS	C₁ ◁ C₈

326 conjugacy classes of subgroups; only the 113 normal subgroups are shown.

normal subgroups only

This group has 326 conjugacy classes of subgroups — too many to draw. Only its 113 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 168

Conjugacy classes & character table

168 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	D₃×M₁₆×AGL(1,𝔽₇), D₃×SD₁₆×AGL(1,𝔽₇), D₃×D₈×AGL(1,𝔽₇), …
maximal normal subgroup of	D₃×M₁₆×AGL(1,𝔽₇), D₃×SD₁₆×AGL(1,𝔽₇), D₃×D₈×AGL(1,𝔽₇)
maximal quotient of	AGL(1,𝔽₇)×#3710

GAP

Past the SmallGroups library coverage — no SmallGroups id.