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C₂×D₇×C₁₇×ΓL(1,𝔽₈) #23756226

order	9996
automorphism	?
homology	Abelianization (H₁) = C₂²×C₃×C₁₇ · Schur multiplier (H₂) = C₂

Aliases

C₂×D₇×C₁₇×ΓL(1,𝔽₈)

Splittings

Subgroups

	subgroup	G/H
center, hypercenter	C₂×C₁₇	D₇×ΓL(1,𝔽₈)
commutator, cosocle, hypocenter	C₇²	C₂²×C₃×C₁₇
Frattini	C₁	G
Fitting, socle	C₂×C₇²×C₁₇	C₂×C₃
LCS	G ▷ C₇²
UCS	C₁ ◁ C₂×C₁₇

84 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

850 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₂×C₁₇×ΓL(1,𝔽₈)×AGL(1,𝔽₇), D₃×D₇×C₁₇×ΓL(1,𝔽₈), C₂×C₃×D₇×C₁₇×ΓL(1,𝔽₈), …
maximal normal subgroup of	C₂×C₁₇×ΓL(1,𝔽₈)×AGL(1,𝔽₇), C₂×C₃×D₇×C₁₇×ΓL(1,𝔽₈)
maximal quotient of	C₂×D₇×C₁₇×C₇⋊C₉, D₃×D₇×C₁₇×ΓL(1,𝔽₈), C₂×C₃×D₇×C₁₇×ΓL(1,𝔽₈), …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(9996, 129);