Finite Group Databasebeta

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C₂²×C₄²×C₁₃×C₁₇ #72192307

order	14144
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) order 28311552
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₂⁵×C₄

Aliases

abelian	C₂²×C₄²×C₁₃×C₁₇
multiplicative	(ℤ/35440)ˣ

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₂²	C₂⁴×C₁₃×C₁₇
socle, prime radical	C₂⁴×C₁₃×C₁₇	C₂²
LCS	G ▷ C₁
UCS	C₁ ◁ G

996 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	C₂²×C₄×C₈×C₁₃×C₁₇, C₂×C₄³×C₁₃×C₁₇, C₂³×C₄²×C₁₃×C₁₇
maximal normal subgroup of	C₂²×C₄×C₈×C₁₃×C₁₇, C₂×C₄³×C₁₃×C₁₇, C₂³×C₄²×C₁₃×C₁₇
maximal quotient of	C₂²×C₄×C₈×C₁₃×C₁₇, C₂×C₄³×C₁₃×C₁₇, C₂³×C₄²×C₁₃×C₁₇

GAP

Past the SmallGroups library coverage — no SmallGroups id.