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#384×C₂₉₃ #34035645

order	18752
nilpotency class	2
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₂₉₃ · Schur multiplier (H₂) = C₂²×C₄

Aliases

#384×C₂₉₃

Subgroups

	subgroup	G/H
center, socle, prime radical	C₂³×C₂₉₃	C₂³
commutator	C₂²	C₂²×C₄×C₂₉₃
Frattini, cosocle	C₂³	C₂³×C₂₉₃
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₂₉₃ ◁ G

186 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 18752

Conjugacy classes & character table

8204 conjugacy classes. The character table is too large to display.

Relationships

Fitting subgroup of	#49156668, #49156731, #49158782, …
maximal subgroup of	#1296×C₂₉₃, #1325×C₂₉₃, #1802×C₂₉₃, …
maximal normal subgroup of	#1296×C₂₉₃, #1325×C₂₉₃, #1802×C₂₉₃, …
maximal quotient of	C₄⋊#95×C₂₉₃, #1444×C₂₉₃, #1842×C₂₉₃, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(18752, 65);