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C₂×D₇×C₁₇² #22549167

order	8092
isoclinism	isoclinic class of D₇
automorphism	?
homology	Abelianization (H₁) = C₂²×C₁₇² · Schur multiplier (H₂) = C₂×C₁₇

Aliases

direct product	C₂×D₇×C₁₇²
unambiguous semidirect product	C₇⋊(C₂²×C₁₇²)
unambiguous semidirect product	(C₂×C₇)⋊(C₂×C₁₇²)

Splittings

Fitting, socle	C₂×C₇×C₁₇² ⋊ C₂
derived, Sylow	C₇ ⋊ C₂²×C₁₇²
Hall	C₇×C₁₇² ⋊ C₂²

Subgroups

	subgroup	G/H
center, hypercenter	C₂×C₁₇²	D₇
commutator, hypocenter	C₇	C₂²×C₁₇²
Frattini	C₁	G
Fitting, socle	C₂×C₇×C₁₇²	C₂
LCS	G ▷ C₇
UCS	C₁ ◁ C₂×C₁₇²

200 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

2890 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₂×D₇⋊(C₁₇²⋊C₃), C₂×C₁₇²×AGL(1,𝔽₇), C₂×D₇×C₁₇²⋊C₃, …
maximal normal subgroup of	C₂×D₇⋊(C₁₇²⋊C₃), C₂×C₁₇²×AGL(1,𝔽₇), C₂×D₇×C₁₇²⋊C₃, …
maximal quotient of	D₃×D₇×C₁₇², C₂×C₃×D₇×C₁₇², C₂×C₁₇²×D₂₁

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(8092, 34);