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#384×C₂₄₁ #29507233

order	15424
nilpotency class	2
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₂₄₁ · Schur multiplier (H₂) = C₂²×C₄

Aliases

#384×C₂₄₁

Subgroups

	subgroup	G/H
center, socle, prime radical	C₂³×C₂₄₁	C₂³
commutator	C₂²	C₂²×C₄×C₂₄₁
Frattini, cosocle	C₂³	C₂³×C₂₄₁
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₂₄₁ ◁ G

186 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 15424

Conjugacy classes & character table

6748 conjugacy classes. The character table is too large to display.

Relationships

Fitting subgroup of	#44505328, #44505391, #44507442, …
maximal subgroup of	#1296×C₂₄₁, #1325×C₂₄₁, #1802×C₂₄₁, …
maximal normal subgroup of	#1296×C₂₄₁, #1325×C₂₄₁, #1802×C₂₄₁, …
maximal quotient of	C₄⋊#95×C₂₄₁, #1444×C₂₄₁, #1842×C₂₄₁, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15424, 65);