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C₃²×C₈×C₁₁₃ #72187017

order	8136
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) order 21504
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₃

Aliases

C₃²×C₈×C₁₁₃

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₄	C₂×C₃²×C₁₁₃
socle, prime radical	C₂×C₃²×C₁₁₃	C₄
LCS	G ▷ C₁
UCS	C₁ ◁ G

48 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

8136 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₃²×C₁₆×C₁₁₃, C₂×C₃²×C₈×C₁₁₃, C₃×C₈×C₉×C₁₁₃, …
maximal normal subgroup of	C₃²×C₁₆×C₁₁₃, C₂×C₃²×C₈×C₁₁₃, C₃×C₈×C₉×C₁₁₃, …
maximal quotient of	C₃²×C₁₆×C₁₁₃, C₂×C₃²×C₈×C₁₁₃, C₃×C₈×C₉×C₁₁₃, …

GAP

Past the SmallGroups library coverage — no SmallGroups id.