Finite Group Databasebeta

← Prev (#72185172) Next (#72185174) →

C₂×C₄×C₉×C₈₃ #72185173

order	5976
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) order 3936
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₂

Aliases

abelian	C₂×C₄×C₉×C₈₃
multiplicative	(ℤ/6179)ˣ, (ℤ/12358)ˣ

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₂×C₃	C₂²×C₃×C₈₃
socle, prime radical	C₂²×C₃×C₈₃	C₂×C₃
LCS	G ▷ C₁
UCS	C₁ ◁ G

48 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

5976 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₂×C₈×C₉×C₈₃, C₄²×C₉×C₈₃, C₂²×C₄×C₉×C₈₃, …
maximal normal subgroup of	C₂×C₈×C₉×C₈₃, C₄²×C₉×C₈₃, C₂²×C₄×C₉×C₈₃, …
maximal quotient of	C₂×C₈×C₉×C₈₃, C₄²×C₉×C₈₃, C₂²×C₄×C₉×C₈₃, …
automorphism group of	C₃₇×C₁₆₇
outer automorphism group of	C₃₇×C₁₆₇

GAP

Past the SmallGroups library coverage — no SmallGroups id.