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C₂³×C₈²×C₃₂ #72194370

order	16384
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) order 4433230883192832
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₂¹²×C₈³

Aliases

C₂³×C₈²×C₃₂

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₄²×C₁₆	C₂⁶
socle, prime radical	C₂⁶	C₄²×C₁₆
LCS	G ▷ C₁
UCS	C₁ ◁ G
LECS	G ▷ C₄²×C₁₆ ▷ C₂²×C₈ ▷ C₄ ▷ C₂ ▷ C₁

523489 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×C₈²×C₆₄, C₂³×C₈×C₁₆×C₃₂, C₂²×C₄×C₈²×C₃₂, …
maximal normal subgroup of	C₂³×C₈²×C₆₄, C₂³×C₈×C₁₆×C₃₂, C₂²×C₄×C₈²×C₃₂, …
maximal quotient of	C₂³×C₈²×C₆₄, C₂³×C₈×C₁₆×C₃₂, C₂²×C₄×C₈²×C₃₂, …

GAP

Past the SmallGroups library coverage — no SmallGroups id.