Finite Group Databasebeta

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C₄²×C₇×C₈×C₁₃ #72190075

order	11648
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) order 7077888
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₄³

Aliases

C₄²×C₇×C₈×C₁₃

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₂²×C₄	C₂³×C₇×C₁₃
socle, prime radical	C₂³×C₇×C₁₃	C₂²×C₄
LCS	G ▷ C₁
UCS	C₁ ◁ G

816 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

11648 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₄²×C₇×C₁₃×C₁₆, C₄×C₇×C₈²×C₁₃, C₂×C₄²×C₇×C₈×C₁₃
maximal normal subgroup of	C₄²×C₇×C₁₃×C₁₆, C₄×C₇×C₈²×C₁₃, C₂×C₄²×C₇×C₈×C₁₃
maximal quotient of	C₄²×C₇×C₁₃×C₁₆, C₄×C₇×C₈²×C₁₃, C₂×C₄²×C₇×C₈×C₁₃

GAP

Past the SmallGroups library coverage — no SmallGroups id.