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C₄²×C₉×C₆₇ #72188369

order	9648
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) order 38016
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₄

Aliases

abelian	C₄²×C₉×C₆₇
multiplicative	(ℤ/9953)ˣ, (ℤ/19906)ˣ

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₂²×C₃	C₂²×C₃×C₆₇
socle, prime radical	C₂²×C₃×C₆₇	C₂²×C₃
LCS	G ▷ C₁
UCS	C₁ ◁ G

90 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	C₄×C₈×C₉×C₆₇, C₂×C₄²×C₉×C₆₇, C₄²×C₂₇×C₆₇, …
maximal normal subgroup of	C₄×C₈×C₉×C₆₇, C₂×C₄²×C₉×C₆₇, C₄²×C₂₇×C₆₇, …
maximal quotient of	C₄×C₈×C₉×C₆₇, C₂×C₄²×C₉×C₆₇, C₄²×C₂₇×C₆₇, …
automorphism group of	C₃₇×C₂₆₉
outer automorphism group of	C₃₇×C₂₆₉

GAP

Past the SmallGroups library coverage — no SmallGroups id.