C₂×C₅³×D₄ #14522930

order	2000
nilpotency class	2
isoclinism	isoclinic class of D₄
automorphism	?
homology	Abelianization (H₁) = C₂³×C₅³ · Schur multiplier (H₂) = C₂³×C₅³

Aliases

direct product	C₂×C₅³×D₄
unambiguous semidirect product	C₄⋊(C₂²×C₅³)
unambiguous semidirect product	C₂²⋊(C₂²×C₅³)
unambiguous semidirect product	C₂³⋊(C₂×C₅³)

	subgroup	G/H
center, socle	C₂²×C₅³	C₂²
commutator, Frattini, cosocle	C₂	C₂³×C₅³
LCS	G ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₅³ ◁ G

1728 conjugacy classes of subgroups.

minimal degree	μ(G) = 21
transitive degree	μ_t(G) = 1000

A minimal faithful permutation representation — 3 generators on 21 points:

(1,2)(7,8,9,10,11);(3,4,5,6)(12,13,14,15,16);(4,6)(17,18,19,20,21)

1250 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2000, 893);