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C₂×C₃×C₈×C₁₇² #72192086

order	13872
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) order 2506752
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₂×C₁₇

Aliases

abelian	C₂×C₃×C₈×C₁₇²
multiplicative	(ℤ/14111)ˣ, (ℤ/28222)ˣ

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₄	C₂²×C₃×C₁₇²
socle, prime radical	C₂²×C₃×C₁₇²	C₄
LCS	G ▷ C₁
UCS	C₁ ◁ G

440 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

13872 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₂×C₃×C₁₆×C₁₇², C₃×C₄×C₈×C₁₇², C₂²×C₃×C₈×C₁₇²
maximal normal subgroup of	C₂×C₃×C₁₆×C₁₇², C₃×C₄×C₈×C₁₇², C₂²×C₃×C₈×C₁₇²
maximal quotient of	C₂×C₃×C₁₆×C₁₇², C₃×C₄×C₈×C₁₇², C₂²×C₃×C₈×C₁₇²
automorphism group of	C₁₀₃×C₁₃₇
outer automorphism group of	C₁₀₃×C₁₃₇

GAP

Past the SmallGroups library coverage — no SmallGroups id.