Finite Group Databasebeta

← Prev (#72188485) Next (#72188487) →

C₂×C₈×C₁₃×C₄₇ #72188486

order	9776
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) order 8832
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₂

Aliases

abelian	C₂×C₈×C₁₃×C₄₇
multiplicative	(ℤ/14667)ˣ, (ℤ/19556)ˣ, (ℤ/29334)ˣ

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₄	C₂²×C₁₃×C₄₇
socle, prime radical	C₂²×C₁₃×C₄₇	C₄
LCS	G ▷ C₁
UCS	C₁ ◁ G

44 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₂×C₁₃×C₁₆×C₄₇, C₄×C₈×C₁₃×C₄₇, C₂²×C₈×C₁₃×C₄₇, …
maximal normal subgroup of	C₂×C₁₃×C₁₆×C₄₇, C₄×C₈×C₁₃×C₄₇, C₂²×C₈×C₁₃×C₄₇, …
maximal quotient of	C₂×C₁₃×C₁₆×C₄₇, C₄×C₈×C₁₃×C₄₇, C₂²×C₈×C₁₃×C₄₇, …

GAP

Past the SmallGroups library coverage — no SmallGroups id.