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C₂×C₃×C₄×C₅₇₇ #72192081

order	13848
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) order 9216
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₂

Aliases

abelian	C₂×C₃×C₄×C₅₇₇
multiplicative	(ℤ/16163)ˣ, (ℤ/17315)ˣ, (ℤ/20781)ˣ, (ℤ/32326)ˣ, (ℤ/34630)ˣ, (ℤ/41562)ˣ

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₂	C₂²×C₃×C₅₇₇
socle, prime radical	C₂²×C₃×C₅₇₇	C₂
LCS	G ▷ C₁
UCS	C₁ ◁ G

32 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

13848 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₂×C₃×C₈×C₅₇₇, C₃×C₄²×C₅₇₇, C₂²×C₃×C₄×C₅₇₇
maximal normal subgroup of	C₂×C₃×C₈×C₅₇₇, C₃×C₄²×C₅₇₇, C₂²×C₃×C₄×C₅₇₇
maximal quotient of	C₂×C₃×C₈×C₅₇₇, C₃×C₄²×C₅₇₇, C₂²×C₃×C₄×C₅₇₇
automorphism group of	C₇×C₂₃₀₉, C₅×C₃₄₆₃
outer automorphism group of	C₇×C₂₃₀₉, C₅×C₃₄₆₃

GAP

Past the SmallGroups library coverage — no SmallGroups id.