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C₂×C₄×C₂₇×C₄₉ #72189165

order	10584
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) order 6048
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₂

Aliases

abelian	C₂×C₄×C₂₇×C₄₉
multiplicative	(ℤ/13235)ˣ, (ℤ/15957)ˣ, (ℤ/26470)ˣ, (ℤ/31914)ˣ

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₂×C₇×C₉	C₂²×C₃×C₇
socle, prime radical	C₂²×C₃×C₇	C₂×C₇×C₉
LCS	G ▷ C₁
UCS	C₁ ◁ G

96 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

10584 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₂×C₈×C₂₇×C₄₉, C₄²×C₂₇×C₄₉, C₂²×C₄×C₂₇×C₄₉, …
maximal normal subgroup of	C₂×C₈×C₂₇×C₄₉, C₄²×C₂₇×C₄₉, C₂²×C₄×C₂₇×C₄₉, …
maximal quotient of	C₂×C₈×C₂₇×C₄₉, C₄²×C₂₇×C₄₉, C₂²×C₄×C₂₇×C₄₉, …
automorphism group of	C₅×C₂₆₄₇, C₂×C₈₁×C₁₉₇
outer automorphism group of	C₅×C₂₆₄₇, C₂×C₈₁×C₁₉₇

GAP

Past the SmallGroups library coverage — no SmallGroups id.