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C₂×#376×C₁₂₇ #30635219

order	16256
nilpotency class	2
isoclinism	isoclinic class of D₄
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄²×C₁₂₇ · Schur multiplier (H₂) = C₂⁴×C₄²

Aliases

C₂×#376×C₁₂₇

Subgroups

	subgroup	G/H
center	C₂³×C₄×C₁₂₇	C₂²
commutator	C₂	C₂²×C₄²×C₁₂₇
Frattini, cosocle	C₂³	C₂⁴×C₁₂₇
socle, prime radical	C₂⁴×C₁₂₇	C₂³
LCS	G ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₄×C₁₂₇ ◁ G

840 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

10160 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₂×C₁₂₇×#1274, C₁₂₇×#7855, C₁₂₇×#7906, …
maximal normal subgroup of	C₂×C₁₂₇×#1274, C₁₂₇×#7855, C₁₂₇×#7906, …
maximal quotient of	C₂×C₄×#95×C₁₂₇, C₄×#376×C₁₂₇, C₂×C₁₂₇×#1434, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(16256, 999);