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C₂²×C₃²×C₁₃×C₁₇ #22547401

order	7956
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) order 55296
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₂×C₃

Aliases

abelian	C₂²×C₃²×C₁₃×C₁₇
multiplicative	(ℤ/8137)ˣ, (ℤ/9289)ˣ, (ℤ/11943)ˣ, (ℤ/16274)ˣ, (ℤ/18578)ˣ, (ℤ/23886)ˣ

Subgroups

	subgroup	G/H
center	G	C₁
commutator, Frattini	C₁	G
LCS	G ▷ C₁
UCS	C₁ ◁ G

120 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

7956 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₂×C₃²×C₄×C₁₃×C₁₇, C₂³×C₃²×C₁₃×C₁₇, C₂²×C₃×C₉×C₁₃×C₁₇, …
maximal normal subgroup of	C₂×C₃²×C₄×C₁₃×C₁₇, C₂³×C₃²×C₁₃×C₁₇, C₂²×C₃×C₉×C₁₃×C₁₇, …
maximal quotient of	C₂×C₃²×C₄×C₁₃×C₁₇, C₂³×C₃²×C₁₃×C₁₇, C₂²×C₃×C₉×C₁₃×C₁₇, …
automorphism group of	C₇₉×C₁₀₃, C₇×C₁₃₂₇
outer automorphism group of	C₇₉×C₁₀₃, C₇×C₁₃₂₇

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(7956, 73);