Finite Group Databasebeta

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C₂×C₄²×C₁₃×C₁₇ #72186144

order	7072
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) order 294912
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₂²×C₄

Aliases

C₂×C₄²×C₁₃×C₁₇

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₂²	C₂³×C₁₃×C₁₇
socle, prime radical	C₂³×C₁₃×C₁₇	C₂²
LCS	G ▷ C₁
UCS	C₁ ◁ G

216 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

7072 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₂×C₄×C₈×C₁₃×C₁₇, C₄³×C₁₃×C₁₇, C₂²×C₄²×C₁₃×C₁₇, …
maximal normal subgroup of	C₂×C₄×C₈×C₁₃×C₁₇, C₄³×C₁₃×C₁₇, C₂²×C₄²×C₁₃×C₁₇, …
maximal quotient of	C₂×C₄×C₈×C₁₃×C₁₇, C₄³×C₁₃×C₁₇, C₂²×C₄²×C₁₃×C₁₇, …

GAP

Past the SmallGroups library coverage — no SmallGroups id.