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#2276×C₁₅₁ #34065608

order	19328
nilpotency class	2
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄²×C₁₅₁ · Schur multiplier (H₂) = C₂⁴×C₄

Aliases

#2276×C₁₅₁

Subgroups

	subgroup	G/H
center, socle, prime radical	C₂³×C₁₅₁	C₂⁴
commutator	C₂	C₂²×C₄²×C₁₅₁
Frattini, cosocle	C₂³	C₂⁴×C₁₅₁
LCS	G ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₅₁ ◁ G

628 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 19328

Conjugacy classes & character table

10268 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₁₅₁×#9324, C₁₅₁×#9326, C₁₅₁×#17549, …
maximal normal subgroup of	C₁₅₁×#9324, C₁₅₁×#9326, C₁₅₁×#17549, …
maximal quotient of	C₁₅₁×#13750, C₁₅₁×#13783, C₁₅₁×#13786, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(19328, 1008);