Finite Group Databasebeta

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C₂×C₁₆×C₁₇×C₂₃ #72190856

order	12512
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) order 11264
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₂

Aliases

abelian	C₂×C₁₆×C₁₇×C₂₃
multiplicative	(ℤ/13583)ˣ, (ℤ/18771)ˣ, (ℤ/25028)ˣ, (ℤ/27166)ˣ, (ℤ/37542)ˣ

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₈	C₂²×C₁₇×C₂₃
socle, prime radical	C₂²×C₁₇×C₂₃	C₈
LCS	G ▷ C₁
UCS	C₁ ◁ G

56 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

12512 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₂×C₁₇×C₂₃×C₃₂, C₄×C₁₆×C₁₇×C₂₃, C₂²×C₁₆×C₁₇×C₂₃
maximal normal subgroup of	C₂×C₁₇×C₂₃×C₃₂, C₄×C₁₆×C₁₇×C₂₃, C₂²×C₁₆×C₁₇×C₂₃
maximal quotient of	C₂×C₁₇×C₂₃×C₃₂, C₄×C₁₆×C₁₇×C₂₃, C₂²×C₁₆×C₁₇×C₂₃

GAP

Past the SmallGroups library coverage — no SmallGroups id.