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#383×C₂₅₇ #30656252

order	16448
nilpotency class	2
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₂₅₇ · Schur multiplier (H₂) = C₂³

Aliases

#383×C₂₅₇

Subgroups

	subgroup	G/H
center, socle, prime radical	C₂³×C₂₅₇	C₂³
commutator	C₂²	C₂²×C₄×C₂₅₇
Frattini, cosocle	C₂³	C₂³×C₂₅₇
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₂₅₇ ◁ G

138 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 16448

Conjugacy classes & character table

7196 conjugacy classes. The character table is too large to display.

Relationships

Fitting subgroup of	#45662184, #45662866, #45662870, …
maximal subgroup of	#1288×C₂₅₇, #1514×C₂₅₇, #1515×C₂₅₇, …
maximal normal subgroup of	#1288×C₂₅₇, #1514×C₂₅₇, #1515×C₂₅₇, …
maximal quotient of	#1434×C₂₅₇, #1443×C₂₅₇, #1839×C₂₅₇, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(16448, 64);