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C₄×C₈×C₁₃×C₁₇ #72186142

order	7072
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) order 24576
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₄

Aliases

abelian	C₄×C₈×C₁₃×C₁₇
multiplicative	(ℤ/7261)ˣ, (ℤ/14522)ˣ

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₂×C₄	C₂²×C₁₃×C₁₇
socle, prime radical	C₂²×C₁₃×C₁₇	C₂×C₄
LCS	G ▷ C₁
UCS	C₁ ◁ G

88 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	C₄×C₁₃×C₁₆×C₁₇, C₈²×C₁₃×C₁₇, C₂×C₄×C₈×C₁₃×C₁₇, …
maximal normal subgroup of	C₄×C₁₃×C₁₆×C₁₇, C₈²×C₁₃×C₁₇, C₂×C₄×C₈×C₁₃×C₁₇, …
maximal quotient of	C₄×C₁₃×C₁₆×C₁₇, C₈²×C₁₃×C₁₇, C₂×C₄×C₈×C₁₃×C₁₇, …
automorphism group of	C₅₃×C₁₃₇
outer automorphism group of	C₅₃×C₁₃₇

GAP

Past the SmallGroups library coverage — no SmallGroups id.