Finite Group Databasebeta

← Prev (#72192116) Next (#72192118) →

C₂³×C₉×C₁₉₃ #72192117

order	13896
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) order 193536
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₂³

Aliases

C₂³×C₉×C₁₉₃

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₃	C₂³×C₃×C₁₉₃
socle, prime radical	C₂³×C₃×C₁₉₃	C₃
LCS	G ▷ C₁
UCS	C₁ ◁ G

96 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

13896 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₂²×C₄×C₉×C₁₉₃, C₂⁴×C₉×C₁₉₃
maximal normal subgroup of	C₂²×C₄×C₉×C₁₉₃, C₂⁴×C₉×C₁₉₃
maximal quotient of	C₂²×C₄×C₉×C₁₉₃, C₂⁴×C₉×C₁₉₃

GAP

Past the SmallGroups library coverage — no SmallGroups id.