Finite Group Databasebeta

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C₂×C₃²×C₈×C₆₄ #72187965

order	9216
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) order 6291456
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₂²×C₃×C₈

Aliases

C₂×C₃²×C₈×C₆₄

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₄×C₃₂	C₂³×C₃²
socle, prime radical	C₂³×C₃²	C₄×C₃₂
LCS	G ▷ C₁
UCS	C₁ ◁ G

1902 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

9216 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₂×C₃²×C₈×C₁₂₈, C₂×C₃²×C₁₆×C₆₄, C₃²×C₄×C₈×C₆₄, …
maximal normal subgroup of	C₂×C₃²×C₈×C₁₂₈, C₂×C₃²×C₁₆×C₆₄, C₃²×C₄×C₈×C₆₄, …
maximal quotient of	C₂×C₃²×C₈×C₁₂₈, C₂×C₃²×C₁₆×C₆₄, C₃²×C₄×C₈×C₆₄, …

GAP

Past the SmallGroups library coverage — no SmallGroups id.