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#384×C₂₃₉ #29504288

order	15296
nilpotency class	2
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₂₃₉ · Schur multiplier (H₂) = C₂²×C₄

Aliases

#384×C₂₃₉

Subgroups

	subgroup	G/H
center, socle, prime radical	C₂³×C₂₃₉	C₂³
commutator	C₂²	C₂²×C₄×C₂₃₉
Frattini, cosocle	C₂³	C₂³×C₂₃₉
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₂₃₉ ◁ G

186 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 15296

Conjugacy classes & character table

6692 conjugacy classes. The character table is too large to display.

Relationships

Fitting subgroup of	#44482431, #44482494, #44484545, …
maximal subgroup of	#1296×C₂₃₉, #1325×C₂₃₉, #1802×C₂₃₉, …
maximal normal subgroup of	#1296×C₂₃₉, #1325×C₂₃₉, #1802×C₂₃₉, …
maximal quotient of	C₄⋊#95×C₂₃₉, #1444×C₂₃₉, #1842×C₂₃₉, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15296, 65);