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C₂³×C₄×C₃₁₁ #23755607

order	9952
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) order 6666240
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₂⁶

Aliases

C₂³×C₄×C₃₁₁

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₂	C₂⁴×C₃₁₁
socle, prime radical	C₂⁴×C₃₁₁	C₂
LCS	G ▷ C₁
UCS	C₁ ◁ G

236 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

9952 conjugacy classes. The character table is too large to display.

Relationships

Fitting subgroup of	C₂×C₃₁₁⋊#95, C₄×C₂²⋊Dic₃₁₁, #34091554, …
maximal subgroup of	C₂×#95×C₃₁₁, C₄×C₂²⋊C₄×C₃₁₁, #380×C₃₁₁, …
maximal normal subgroup of	C₂×#95×C₃₁₁, C₄×C₂²⋊C₄×C₃₁₁, #380×C₃₁₁, …
maximal quotient of	C₂²×C₄²×C₃₁₁, C₂²×C₂²⋊C₄×C₃₁₁, C₂²×C₄⋊C₄×C₃₁₁, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(9952, 45);