Finite Group Databasebeta

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C₂²×C₄×C₇×C₈×C₁₃ #72190077

order	11648
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) order 14155776
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₂⁵×C₄

Aliases

C₂²×C₄×C₇×C₈×C₁₃

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₂×C₄	C₂⁴×C₇×C₁₃
socle, prime radical	C₂⁴×C₇×C₁₃	C₂×C₄
LCS	G ▷ C₁
UCS	C₁ ◁ G

1520 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	C₂²×C₄×C₇×C₁₃×C₁₆, C₂²×C₇×C₈²×C₁₃, C₂×C₄²×C₇×C₈×C₁₃, …
maximal normal subgroup of	C₂²×C₄×C₇×C₁₃×C₁₆, C₂²×C₇×C₈²×C₁₃, C₂×C₄²×C₇×C₈×C₁₃, …
maximal quotient of	C₂²×C₄×C₇×C₁₃×C₁₆, C₂²×C₇×C₈²×C₁₃, C₂×C₄²×C₇×C₈×C₁₃, …

GAP

Past the SmallGroups library coverage — no SmallGroups id.