Finite Group Databasebeta

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C₂×C₄²×C₇×C₆₄ #72192467

order	14336
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) order 301989888
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₂³×C₄³

Aliases

abelian	C₂×C₄²×C₇×C₆₄
multiplicative	(ℤ/35920)ˣ, (ℤ/37120)ˣ

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₂²×C₃₂	C₂⁴×C₇
socle, prime radical	C₂⁴×C₇	C₂²×C₃₂
LCS	G ▷ C₁
UCS	C₁ ◁ G

4368 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

14336 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₂×C₄²×C₇×C₁₂₈, C₂×C₄×C₇×C₈×C₆₄, C₄³×C₇×C₆₄, …
maximal normal subgroup of	C₂×C₄²×C₇×C₁₂₈, C₂×C₄×C₇×C₈×C₆₄, C₄³×C₇×C₆₄, …
maximal quotient of	C₂×C₄²×C₇×C₁₂₈, C₂×C₄×C₇×C₈×C₆₄, C₄³×C₇×C₆₄, …

GAP

Past the SmallGroups library coverage — no SmallGroups id.