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C₃²×C₈×C₁₃₇ #72188570

order	9864
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) order 26112
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₃

Aliases

C₃²×C₈×C₁₃₇

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₄	C₂×C₃²×C₁₃₇
socle, prime radical	C₂×C₃²×C₁₃₇	C₄
LCS	G ▷ C₁
UCS	C₁ ◁ G

48 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

9864 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₃²×C₁₆×C₁₃₇, C₂×C₃²×C₈×C₁₃₇, C₃×C₈×C₉×C₁₃₇, …
maximal normal subgroup of	C₃²×C₁₆×C₁₃₇, C₂×C₃²×C₈×C₁₃₇, C₃×C₈×C₉×C₁₃₇, …
maximal quotient of	C₃²×C₁₆×C₁₃₇, C₂×C₃²×C₈×C₁₃₇, C₃×C₈×C₉×C₁₃₇, …

GAP

Past the SmallGroups library coverage — no SmallGroups id.