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C₃²×C₁₇×C₆₄ #72188491

order	9792
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) order 24576
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₃

Aliases

C₃²×C₁₇×C₆₄

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₃₂	C₂×C₃²×C₁₇
socle, prime radical	C₂×C₃²×C₁₇	C₃₂
LCS	G ▷ C₁
UCS	C₁ ◁ G

84 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

9792 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₃²×C₁₇×C₁₂₈, C₂×C₃²×C₁₇×C₆₄, C₃×C₉×C₁₇×C₆₄, …
maximal normal subgroup of	C₃²×C₁₇×C₁₂₈, C₂×C₃²×C₁₇×C₆₄, C₃×C₉×C₁₇×C₆₄, …
maximal quotient of	C₃²×C₁₇×C₁₂₈, C₂×C₃²×C₁₇×C₆₄, C₃×C₉×C₁₇×C₆₄, …

GAP

Past the SmallGroups library coverage — no SmallGroups id.