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C₂³×C₄×C₁₇×C₂₇ #72192802

order	14688
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) order 6193152
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₂⁶

Aliases

abelian	C₂³×C₄×C₁₇×C₂₇
multiplicative	(ℤ/36760)ˣ, (ℤ/44112)ˣ, (ℤ/55140)ˣ

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₂×C₉	C₂⁴×C₃×C₁₇
socle, prime radical	C₂⁴×C₃×C₁₇	C₂×C₉
LCS	G ▷ C₁
UCS	C₁ ◁ G

944 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

14688 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₂³×C₈×C₁₇×C₂₇, C₂²×C₄²×C₁₇×C₂₇, C₂⁴×C₄×C₁₇×C₂₇
maximal normal subgroup of	C₂³×C₈×C₁₇×C₂₇, C₂²×C₄²×C₁₇×C₂₇, C₂⁴×C₄×C₁₇×C₂₇
maximal quotient of	C₂³×C₈×C₁₇×C₂₇, C₂²×C₄²×C₁₇×C₂₇, C₂⁴×C₄×C₁₇×C₂₇

GAP

Past the SmallGroups library coverage — no SmallGroups id.