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C₈×C₉²×C₁₉ #72190706

order	12312
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) order 279936
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₉

Aliases

C₈×C₉²×C₁₉

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₃²×C₄	C₂×C₃²×C₁₉
socle, prime radical	C₂×C₃²×C₁₉	C₃²×C₄
LCS	G ▷ C₁
UCS	C₁ ◁ G

184 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

12312 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₉²×C₁₆×C₁₉, C₂×C₈×C₉²×C₁₉
maximal normal subgroup of	C₉²×C₁₆×C₁₉, C₂×C₈×C₉²×C₁₉
maximal quotient of	C₉²×C₁₆×C₁₉, C₂×C₈×C₉²×C₁₉

GAP

Past the SmallGroups library coverage — no SmallGroups id.