Finite Group Databasebeta

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C₇×C₈×C₁₃×C₁₆ #72190070

order	11648
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) order 147456
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₈

Aliases

C₇×C₈×C₁₃×C₁₆

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₄×C₈	C₂²×C₇×C₁₃
socle, prime radical	C₂²×C₇×C₁₃	C₄×C₈
LCS	G ▷ C₁
UCS	C₁ ◁ G

208 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	C₇×C₈×C₁₃×C₃₂, C₇×C₁₃×C₁₆², C₂×C₇×C₈×C₁₃×C₁₆
maximal normal subgroup of	C₇×C₈×C₁₃×C₃₂, C₇×C₁₃×C₁₆², C₂×C₇×C₈×C₁₃×C₁₆
maximal quotient of	C₇×C₈×C₁₃×C₃₂, C₇×C₁₃×C₁₆², C₂×C₇×C₈×C₁₃×C₁₆

GAP

Past the SmallGroups library coverage — no SmallGroups id.