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C₂×D₇×AΣL(1,𝔽₁₆) #13506505

order	1792
automorphism	?
homology	Abelianization (H₁) = C₂³×C₄ · Schur multiplier (H₂) = C₂⁷

Aliases

C₂×D₇×AΣL(1,𝔽₁₆)

Splittings

Fitting	C₂×C₇×AΣL(1,𝔽₁₆) ⋊ C₂
Sylow	C₇ ⋊ C₂²×AΣL(1,𝔽₁₆)

Subgroups

	subgroup	G/H
center	C₂²	D₇×#99
commutator	C₂³×C₇	C₂³×C₄
Frattini	C₂×D₄	C₂³×D₇
Fitting	C₂×C₇×AΣL(1,𝔽₁₆)	C₂
socle	C₂²×C₇	C₂×#99
prime radical	C₂×D₇×#120	C₂
cosocle	C₂×C₇×D₄	C₂⁴
hypercenter	C₂×AΣL(1,𝔽₁₆)	D₇
hypocenter	C₇	C₂²×AΣL(1,𝔽₁₆)
LCS	G ▷ C₂³×C₇ ▷ C₂²×C₇ ▷ C₂×C₇ ▷ C₇
UCS	C₁ ◁ C₂² ◁ C₂³ ◁ C₂²×D₄ ◁ C₂×AΣL(1,𝔽₁₆)

2774 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 112

Conjugacy classes & character table

130 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₂×AGL(1,𝔽₇)×AΣL(1,𝔽₁₆), D₇×#12687, D₇×#13343
maximal normal subgroup of	C₂×AGL(1,𝔽₇)×AΣL(1,𝔽₁₆), D₇×#12687, D₇×#13343
maximal quotient of	D₇×#12687

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1792, 322277);