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C₂⁴×C₃×C₄×C₃₇ #72186163

order	7104
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) order 743178240
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₂¹⁰

Aliases

abelian	C₂⁴×C₃×C₄×C₃₇
multiplicative	(ℤ/25032)ˣ, (ℤ/26760)ˣ

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₂	C₂⁵×C₃×C₃₇
socle, prime radical	C₂⁵×C₃×C₃₇	C₂
LCS	G ▷ C₁
UCS	C₁ ◁ G

2724 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

7104 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₂⁴×C₃×C₈×C₃₇, C₂³×C₃×C₄²×C₃₇, C₂⁵×C₃×C₄×C₃₇, …
maximal normal subgroup of	C₂⁴×C₃×C₈×C₃₇, C₂³×C₃×C₄²×C₃₇, C₂⁵×C₃×C₄×C₃₇, …
maximal quotient of	C₂⁴×C₃×C₈×C₃₇, C₂³×C₃×C₄²×C₃₇, C₂⁵×C₃×C₄×C₃₇, …
automorphism group of	C₃×C₇×C₈×C₁₄₉, C₃×C₅×C₈×C₂₂₃
outer automorphism group of	C₃×C₇×C₈×C₁₄₉, C₃×C₅×C₈×C₂₂₃

GAP

Past the SmallGroups library coverage — no SmallGroups id.