Finite Group Databasebeta

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C₂×C₅²×C₁₃×C₁₆ #72189059

order	10400
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) order 184320
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₂×C₅

Aliases

C₂×C₅²×C₁₃×C₁₆

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₈	C₂²×C₅²×C₁₃
socle, prime radical	C₂²×C₅²×C₁₃	C₈
LCS	G ▷ C₁
UCS	C₁ ◁ G

224 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

10400 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₂×C₅²×C₁₃×C₃₂, C₄×C₅²×C₁₃×C₁₆, C₂²×C₅²×C₁₃×C₁₆, …
maximal normal subgroup of	C₂×C₅²×C₁₃×C₃₂, C₄×C₅²×C₁₃×C₁₆, C₂²×C₅²×C₁₃×C₁₆, …
maximal quotient of	C₂×C₅²×C₁₃×C₃₂, C₄×C₅²×C₁₃×C₁₆, C₂²×C₅²×C₁₃×C₁₆, …

GAP

Past the SmallGroups library coverage — no SmallGroups id.