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#330×C₁₅₁ #23751674

order	9664
nilpotency class	3
isoclinism	isoclinic class of #327
automorphism	?
homology	Abelianization (H₁) = C₂×C₄×C₁₅₁ · Schur multiplier (H₂) = C₁

Aliases

#330×C₁₅₁

Subgroups

	subgroup	G/H
center, socle, prime radical	C₂²×C₁₅₁	C₂²⋊C₄
commutator	C₂×C₄	C₂×C₄×C₁₅₁
Frattini, cosocle	C₄²	C₂²×C₁₅₁
LCS	G ▷ C₂×C₄ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₅₁ ◁ C₄²×C₁₅₁ ◁ G

60 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

2869 conjugacy classes. The character table is too large to display.

Relationships

Fitting subgroup of	#330×D₁₅₁, #34067697, #34067703, …
maximal subgroup of	C₂×#330×C₁₅₁, #1524×C₁₅₁, #1526×C₁₅₁, …
maximal normal subgroup of	C₂×#330×C₁₅₁, #1524×C₁₅₁, #1526×C₁₅₁, …
maximal quotient of	#1271×C₁₅₁, #1295×C₁₅₁, C₂×#330×C₁₅₁

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(9664, 11);