Finite Group Databasebeta

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C₇×C₈²×C₁₉ #72187387

order	8512
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) order 165888
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₈

Aliases

C₇×C₈²×C₁₉

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₄²	C₂²×C₇×C₁₉
socle, prime radical	C₂²×C₇×C₁₉	C₄²
LCS	G ▷ C₁
UCS	C₁ ◁ G

148 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

8512 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₇×C₈×C₁₆×C₁₉, C₂×C₇×C₈²×C₁₉, C₃×C₇×C₈²×C₁₉
maximal normal subgroup of	C₇×C₈×C₁₆×C₁₉, C₂×C₇×C₈²×C₁₉, C₃×C₇×C₈²×C₁₉
maximal quotient of	C₇×C₈×C₁₆×C₁₉, C₂×C₇×C₈²×C₁₉, C₃×C₇×C₈²×C₁₉

GAP

Past the SmallGroups library coverage — no SmallGroups id.