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C₂²×C₄×C₉×C₆₇ #72188371

order	9648
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) order 76032
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₂³

Aliases

abelian	C₂²×C₄×C₉×C₆₇
multiplicative	(ℤ/15333)ˣ, (ℤ/20444)ˣ, (ℤ/29052)ˣ, (ℤ/30666)ˣ

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₂×C₃	C₂³×C₃×C₆₇
socle, prime radical	C₂³×C₃×C₆₇	C₂×C₃
LCS	G ▷ C₁
UCS	C₁ ◁ G

162 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

9648 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₂²×C₈×C₉×C₆₇, C₂×C₄²×C₉×C₆₇, C₂³×C₄×C₉×C₆₇, …
maximal normal subgroup of	C₂²×C₈×C₉×C₆₇, C₂×C₄²×C₉×C₆₇, C₂³×C₄×C₉×C₆₇, …
maximal quotient of	C₂²×C₈×C₉×C₆₇, C₂×C₄²×C₉×C₆₇, C₂³×C₄×C₉×C₆₇, …
automorphism group of	C₄×C₂₇×C₂₆₉
outer automorphism group of	C₄×C₂₇×C₂₆₉

GAP

Past the SmallGroups library coverage — no SmallGroups id.