Finite Group Databasebeta

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C₂×#72210036 #72252241

order	2048
nilpotency class	3
automorphism	?
homology	Abelianization (H₁) = C₂⁶ · Schur multiplier (H₂) = C₂¹³×C₄²

Aliases

C₂×#72210036

Subgroups

	subgroup	G/H
center, socle	C₂³	#35346
commutator, Frattini, cosocle	C₂⁵	C₂⁶
prime radical	C₂²×H(7,𝔽₂)	C₂²
LCS	G ▷ C₂⁵ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³ ◁ C₂⁶ ◁ G
LECS	G ▷ C₂⁵ ▷ C₂ ▷ C₁

154096 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 256

Conjugacy classes & character table

164 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	#72252252
maximal normal subgroup of	#72252252

GAP

Past the SmallGroups library coverage — no SmallGroups id.