Finite Group Databasebeta

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C₂³×C₈×C₁₃×C₁₇ #72192305

order	14144
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) order 8257536
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₂⁶

Aliases

abelian	C₂³×C₈×C₁₃×C₁₇
multiplicative	(ℤ/42528)ˣ

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₄	C₂⁴×C₁₃×C₁₇
socle, prime radical	C₂⁴×C₁₃×C₁₇	C₄
LCS	G ▷ C₁
UCS	C₁ ◁ G

676 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

14144 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₂³×C₁₃×C₁₆×C₁₇, C₂²×C₄×C₈×C₁₃×C₁₇, C₂⁴×C₈×C₁₃×C₁₇
maximal normal subgroup of	C₂³×C₁₃×C₁₆×C₁₇, C₂²×C₄×C₈×C₁₃×C₁₇, C₂⁴×C₈×C₁₃×C₁₇
maximal quotient of	C₂³×C₁₃×C₁₆×C₁₇, C₂²×C₄×C₈×C₁₃×C₁₇, C₂⁴×C₈×C₁₃×C₁₇

GAP

Past the SmallGroups library coverage — no SmallGroups id.