Finite Group Databasebeta

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C₁₃×C₁₆×C₄₇ #72188485

order	9776
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) = C₂²×C₃×C₄²×C₂₃ (order 4416) · Inn(G) = C₁ · Out(G) = C₂²×C₃×C₄²×C₂₃
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₁

Aliases

cyclic	C₉₇₇₆
abelian	C₁₃×C₁₆×C₄₇

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₈	C₂×C₁₃×C₄₇
socle, prime radical	C₂×C₁₃×C₄₇	C₈
LCS	G ▷ C₁
UCS	C₁ ◁ G

20 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

9776 conjugacy classes. The character table is too large to display.

Relationships

derived subgroup of	Dic₉₇₇₆, D₁₉₅₅₂
maximal subgroup of	C₁₃×C₃₂×C₄₇, C₂×C₁₃×C₁₆×C₄₇, C₃×C₁₃×C₁₆×C₄₇, …
maximal normal subgroup of	C₁₃×C₃₂×C₄₇, C₂×C₁₃×C₁₆×C₄₇, C₃×C₁₃×C₁₆×C₄₇, …
maximal quotient of	C₁₃×C₃₂×C₄₇, C₂×C₁₃×C₁₆×C₄₇, C₃×C₁₃×C₁₆×C₄₇

GAP

Past the SmallGroups library coverage — no SmallGroups id.