Finite Group Databasebeta

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C₂×#72214479 #72255116

order	2048
nilpotency class	4
automorphism	?
homology	Abelianization (H₁) = C₂⁵ · Schur multiplier (H₂) = C₂¹²

Aliases

C₂×#72214479

Subgroups

	subgroup	G/H
center, socle	C₂³	C₂×#2021
commutator, Frattini, cosocle	C₂³×Q₈	C₂⁵
LCS	G ▷ C₂³×Q₈ ▷ C₂³ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³ ◁ C₂⁴×C₄ ◁ C₂⁴×#41 ◁ G
LECS	G ▷ C₂³×Q₈ ▷ C₂³ ▷ C₂ ▷ C₁

67588 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 64

Conjugacy classes & character table

152 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₂×#72214572
maximal normal subgroup of	C₂×#72214572

GAP

Past the SmallGroups library coverage — no SmallGroups id.