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C₂²×C₃×C₄×C₁₇² #72192090

order	13872
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) order 30081024
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₂³×C₁₇

Aliases

C₂²×C₃×C₄×C₁₇²

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₂	C₂³×C₃×C₁₇²
socle, prime radical	C₂³×C₃×C₁₇²	C₂
LCS	G ▷ C₁
UCS	C₁ ◁ G

1080 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	C₂²×C₃×C₈×C₁₇², C₂×C₃×C₄²×C₁₇², C₂³×C₃×C₄×C₁₇²
maximal normal subgroup of	C₂²×C₃×C₈×C₁₇², C₂×C₃×C₄²×C₁₇², C₂³×C₃×C₄×C₁₇²
maximal quotient of	C₂²×C₃×C₈×C₁₇², C₂×C₃×C₄²×C₁₇², C₂³×C₃×C₄×C₁₇²

GAP

Past the SmallGroups library coverage — no SmallGroups id.