Finite Group Databasebeta

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C₂×#7667013 #72299136

order	1024
nilpotency class	2
automorphism	?
homology	Abelianization (H₁) = C₂⁷ · Schur multiplier (H₂) = C₂¹⁹

Aliases

Subgroups

	subgroup	G/H
center, socle	C₂³×C₄	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁷
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂³×C₄ ◁ G
LECS	G ▷ C₂³ ▷ C₁

63629 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 256

Conjugacy classes & character table

256 conjugacy classes — view the full character table.

Relationships

Fitting subgroup of	C₂×#72237719, #72340855, #72340858, …
maximal subgroup of	C₂×#72236189, C₂²×#7667013, #72311826, …
maximal normal subgroup of	C₂×#72236189, C₂²×#7667013, #72311826, …
maximal quotient of	C₂×#72297597, C₂×#72282047, C₂²×#7667013

GAP

Past the SmallGroups library coverage — no SmallGroups id.