C₂×#23897 #6437460

order	512
nilpotency class	3
isoclinism	isoclinic class of #23897
automorphism	?
homology	Abelianization (H₁) = C₂⁵ · Schur multiplier (H₂) = C₂¹¹

Aliases

Borel	B(3,ℤ/4)
direct product	C₂×#23897

	subgroup	G/H
center, socle	C₂²	#2403
commutator, Frattini, cosocle	C₂²×C₄	C₂⁵
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂² ◁ C₂³×C₄ ◁ G
LECS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁

7096 conjugacy classes of subgroups.

minimal degree	μ(G) = 18
transitive degree	μ_t(G) = 32

A minimal faithful permutation representation — 5 generators on 18 points:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 6344656);