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C₂²×C₄×C₁₃×C₃₇ #72186633

order	7696
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) order 82944
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₂³

Aliases

C₂²×C₄×C₁₃×C₃₇

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₂	C₂³×C₁₃×C₃₇
socle, prime radical	C₂³×C₁₃×C₃₇	C₂
LCS	G ▷ C₁
UCS	C₁ ◁ G

108 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

7696 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₂²×C₈×C₁₃×C₃₇, C₂×C₄²×C₁₃×C₃₇, C₂³×C₄×C₁₃×C₃₇, …
maximal normal subgroup of	C₂²×C₈×C₁₃×C₃₇, C₂×C₄²×C₁₃×C₃₇, C₂³×C₄×C₁₃×C₃₇, …
maximal quotient of	C₂²×C₈×C₁₃×C₃₇, C₂×C₄²×C₁₃×C₃₇, C₂³×C₄×C₁₃×C₃₇, …

GAP

Past the SmallGroups library coverage — no SmallGroups id.