C₂₃×C₂²⋊#401 #19162453

order	5888
nilpotency class	2
isoclinism	isoclinic class of #14715
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₂₃ · Schur multiplier (H₂) = C₂⁵

Aliases

direct product	C₂₃×C₂²⋊#401
unambiguous semidirect product	C₂²⋊(C₂₃×#401)

	subgroup	G/H
center, socle	C₂⁴×C₂₃	C₂⁴
commutator, Frattini, cosocle	C₂⁴	C₂⁴×C₂₃
prime radical	C₂⁵×C₂₃	C₂³
LCS	G ▷ C₂⁴ ▷ C₁
UCS	C₁ ◁ C₂⁴×C₂₃ ◁ G

1650 conjugacy classes of subgroups.

1472 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(5888, 7815);