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C₁₂₇×#2955 #30635907

order	16256
nilpotency class	3
automorphism	?
homology	Abelianization (H₁) = C₂³×C₄×C₁₂₇ · Schur multiplier (H₂) = C₂⁵

Aliases

C₁₂₇×#2955

Subgroups

	subgroup	G/H
center	C₈×C₁₂₇	C₂×D₄
commutator	C₄	C₂³×C₄×C₁₂₇
Frattini, cosocle	C₂×C₄	C₂⁴×C₁₂₇
socle	C₂×C₁₂₇	C₂×C₄×D₄
prime radical	#575×C₁₂₇	C₂
LCS	G ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₈×C₁₂₇ ◁ C₂²×C₈×C₁₂₇ ◁ G

456 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

5588 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₁₂₇×#12979, C₁₂₇×#12987, C₁₂₇×#13198, …
maximal normal subgroup of	C₁₂₇×#12979, C₁₂₇×#12987, C₁₂₇×#13198, …
maximal quotient of	C₈×AGL(1,ℤ/8)×C₁₂₇, C₈×#137×C₁₂₇, C₁₂₇×#17869, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(16256, 1687);