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C₃×C₁₃×C₁₆² #72188642

order	9984
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) order 589824
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₁₆

Aliases

C₃×C₁₃×C₁₆²

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₈²	C₂²×C₃×C₁₃
socle, prime radical	C₂²×C₃×C₁₃	C₈²
LCS	G ▷ C₁
UCS	C₁ ◁ G

332 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

9984 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₃×C₁₃×C₁₆×C₃₂, C₂×C₃×C₁₃×C₁₆², C₉×C₁₃×C₁₆², …
maximal normal subgroup of	C₃×C₁₃×C₁₆×C₃₂, C₂×C₃×C₁₃×C₁₆², C₉×C₁₃×C₁₆², …
maximal quotient of	C₃×C₁₃×C₁₆×C₃₂, C₂×C₃×C₁₃×C₁₆², C₉×C₁₃×C₁₆², …

GAP

Past the SmallGroups library coverage — no SmallGroups id.