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#383×C₂₈₃ #31825980

order	18112
nilpotency class	2
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₂₈₃ · Schur multiplier (H₂) = C₂³

Aliases

#383×C₂₈₃

Subgroups

	subgroup	G/H
center, socle, prime radical	C₂³×C₂₈₃	C₂³
commutator	C₂²	C₂²×C₄×C₂₈₃
Frattini, cosocle	C₂³	C₂³×C₂₈₃
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₂₈₃ ◁ G

138 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 18112

Conjugacy classes & character table

7924 conjugacy classes. The character table is too large to display.

Relationships

Fitting subgroup of	#49119125, #49119807, #49119811, …
maximal subgroup of	#1288×C₂₈₃, #1514×C₂₈₃, #1515×C₂₈₃, …
maximal normal subgroup of	#1288×C₂₈₃, #1514×C₂₈₃, #1515×C₂₈₃, …
maximal quotient of	#1434×C₂₈₃, #1443×C₂₈₃, #1839×C₂₈₃, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(18112, 64);