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C₂³×C₄²×C₈×C₁₆ #72194396

order	16384
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) order ≥ 2⁶³
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₂¹⁵×C₄⁵×C₈

Aliases

C₂³×C₄²×C₈×C₁₆

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₂²×C₄×C₈	C₂⁷
socle, prime radical	C₂⁷	C₂²×C₄×C₈
LCS	G ▷ C₁
UCS	C₁ ◁ G
LECS	G ▷ C₂²×C₄×C₈ ▷ C₂×C₄ ▷ C₂ ▷ C₁

7516833 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

16384 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₂³×C₄²×C₈×C₃₂, C₂³×C₄×C₈²×C₁₆, C₂³×C₄²×C₁₆², …
maximal normal subgroup of	C₂³×C₄²×C₈×C₃₂, C₂³×C₄×C₈²×C₁₆, C₂³×C₄²×C₁₆², …
maximal quotient of	C₂³×C₄²×C₈×C₃₂, C₂³×C₄×C₈²×C₁₆, C₂³×C₄²×C₁₆², …

GAP

Past the SmallGroups library coverage — no SmallGroups id.