Finite Group Databasebeta

← Prev (#72192114) Next (#72192116) →

C₂×C₄×C₉×C₁₉₃ #72192115

order	13896
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) order 9216
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₂

Aliases

abelian	C₂×C₄×C₉×C₁₉₃
multiplicative	(ℤ/14687)ˣ, (ℤ/20847)ˣ, (ℤ/20871)ˣ, (ℤ/27796)ˣ, (ℤ/29374)ˣ, (ℤ/41694)ˣ, (ℤ/41742)ˣ

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₂×C₃	C₂²×C₃×C₁₉₃
socle, prime radical	C₂²×C₃×C₁₉₃	C₂×C₃
LCS	G ▷ C₁
UCS	C₁ ◁ G

48 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	C₂×C₈×C₉×C₁₉₃, C₄²×C₉×C₁₉₃, C₂²×C₄×C₉×C₁₉₃
maximal normal subgroup of	C₂×C₈×C₉×C₁₉₃, C₄²×C₉×C₁₉₃, C₂²×C₄×C₉×C₁₉₃
maximal quotient of	C₂×C₈×C₉×C₁₉₃, C₄²×C₉×C₁₉₃, C₂²×C₄×C₉×C₁₉₃
automorphism group of	C₁₉×C₇₇₃
outer automorphism group of	C₁₉×C₇₇₃

GAP

Past the SmallGroups library coverage — no SmallGroups id.