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C₂×H(3,ℤ/4)×C₁₂₇ #30634682

order	16256
nilpotency class	2
isoclinism	isoclinic class of H(3,ℤ/4)
automorphism	?
homology	Abelianization (H₁) = C₂×C₄²×C₁₂₇ · Schur multiplier (H₂) = C₂³×C₄

Aliases

C₂×H(3,ℤ/4)×C₁₂₇

Subgroups

	subgroup	G/H
center	C₂×C₄×C₁₂₇	C₄²
commutator	C₄	C₂×C₄²×C₁₂₇
Frattini, cosocle	C₂²×C₄	C₂³×C₁₂₇
socle	C₂²×C₁₂₇	#95
prime radical	C₂⁴×C₁₂₇	D₄
LCS	G ▷ C₄ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₁₂₇ ◁ G

404 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×#7254, C₁₂₇×#7256, C₄×H(3,ℤ/4)×C₁₂₇, …
maximal normal subgroup of	C₁₂₇×#7254, C₁₂₇×#7256, C₄×H(3,ℤ/4)×C₁₂₇, …
maximal quotient of	C₂×C₁₂₇×#1274, C₁₂₇×#7854, C₁₂₇×#7855, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(16256, 462);