Finite Group Databasebeta

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C₂³×C₄×C₈×C₆₄ #72194351

order	16384
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) order 184717953466368
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₂¹²×C₄²×C₈

Aliases

C₂³×C₄×C₈×C₆₄

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₂×C₄×C₃₂	C₂⁶
socle, prime radical	C₂⁶	C₂×C₄×C₃₂
LCS	G ▷ C₁
UCS	C₁ ◁ G
LECS	G ▷ C₂×C₄×C₃₂ ▷ C₂×C₁₆ ▷ C₈ ▷ C₄ ▷ C₂ ▷ C₁

263905 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×C₄×C₈×C₁₂₈, C₂³×C₄×C₁₆×C₆₄, C₂³×C₈²×C₆₄, …
maximal normal subgroup of	C₂³×C₄×C₈×C₁₂₈, C₂³×C₄×C₁₆×C₆₄, C₂³×C₈²×C₆₄, …
maximal quotient of	C₂³×C₄×C₈×C₁₂₈, C₂³×C₄×C₁₆×C₆₄, C₂³×C₈²×C₆₄, …

GAP

Past the SmallGroups library coverage — no SmallGroups id.