Finite Group Databasebeta

← Prev (#72186450) Next (#72186452) →

C₂×C₉×C₁₃×C₃₂ #72186451

order	7488
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) order 4608
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₂

Aliases

C₂×C₉×C₁₃×C₃₂

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₃×C₁₆	C₂²×C₃×C₁₃
socle, prime radical	C₂²×C₃×C₁₃	C₃×C₁₆
LCS	G ▷ C₁
UCS	C₁ ◁ G

102 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

7488 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₂×C₉×C₁₃×C₆₄, C₄×C₉×C₁₃×C₃₂, C₂²×C₉×C₁₃×C₃₂, …
maximal normal subgroup of	C₂×C₉×C₁₃×C₆₄, C₄×C₉×C₁₃×C₃₂, C₂²×C₉×C₁₃×C₃₂, …
maximal quotient of	C₂×C₉×C₁₃×C₆₄, C₄×C₉×C₁₃×C₃₂, C₂²×C₉×C₁₃×C₃₂, …

GAP

Past the SmallGroups library coverage — no SmallGroups id.