Finite Group Databasebeta

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C₂×C₃²×C₄×C₁₅₇ #72189804

order	11304
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) order 59904
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₂×C₃

Aliases

C₂×C₃²×C₄×C₁₅₇

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₂	C₂²×C₃²×C₁₅₇
socle, prime radical	C₂²×C₃²×C₁₅₇	C₂
LCS	G ▷ C₁
UCS	C₁ ◁ G

96 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

11304 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₂×C₃²×C₈×C₁₅₇, C₃²×C₄²×C₁₅₇, C₂²×C₃²×C₄×C₁₅₇
maximal normal subgroup of	C₂×C₃²×C₈×C₁₅₇, C₃²×C₄²×C₁₅₇, C₂²×C₃²×C₄×C₁₅₇
maximal quotient of	C₂×C₃²×C₈×C₁₅₇, C₃²×C₄²×C₁₅₇, C₂²×C₃²×C₄×C₁₅₇

GAP

Past the SmallGroups library coverage — no SmallGroups id.