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#391×C₂₉₃ #34035652

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

Aliases

#391×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	#49156611, #49156719, #49156912, …
maximal subgroup of	#1272×C₂₉₃, #1319×C₂₉₃, #1394×C₂₉₃, …
maximal normal subgroup of	#1272×C₂₉₃, #1319×C₂₉₃, #1394×C₂₉₃, …
maximal quotient of	C₄⋊#95×C₂₉₃, #1436×C₂₉₃, #1441×C₂₉₃, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(18752, 72);