Finite Group Databasebeta

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C₂×C₈×C₁₃×C₄₉ #72188809

order	10192
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) order 8064
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₂

Aliases

C₂×C₈×C₁₃×C₄₉

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₄×C₇	C₂²×C₇×C₁₃
socle, prime radical	C₂²×C₇×C₁₃	C₄×C₇
LCS	G ▷ C₁
UCS	C₁ ◁ G

66 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

10192 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₂×C₁₃×C₁₆×C₄₉, C₄×C₈×C₁₃×C₄₉, C₂²×C₈×C₁₃×C₄₉, …
maximal normal subgroup of	C₂×C₁₃×C₁₆×C₄₉, C₄×C₈×C₁₃×C₄₉, C₂²×C₈×C₁₃×C₄₉, …
maximal quotient of	C₂×C₁₃×C₁₆×C₄₉, C₄×C₈×C₁₃×C₄₉, C₂²×C₈×C₁₃×C₄₉, …

GAP

Past the SmallGroups library coverage — no SmallGroups id.