Finite Group Databasebeta

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C₂×#72223655 #72223751

order	2048
nilpotency class	3
automorphism	?
homology	Abelianization (H₁) = C₂×C₄²×C₈ · Schur multiplier (H₂) = C₂³×C₄²

Aliases

C₂×#72223655

Subgroups

	subgroup	G/H
center	C₂²×C₈	#322
commutator	C₈	C₂×C₄²×C₈
Frattini, cosocle	C₂×#346	C₂⁴
socle	C₂³	C₂×#1313
prime radical	C₂⁴	C₂×#347
LCS	G ▷ C₈ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₈ ◁ C₂×C₄×#346 ◁ G
LECS	G ▷ C₂×#346 ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁

2204 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₂×#72223687
maximal normal subgroup of	C₂×#72223687
maximal quotient of	C₂×C₈×#7333

GAP

Past the SmallGroups library coverage — no SmallGroups id.