C₂³×C₅×C₂²⋊Q₈ #11985377

order	1280
nilpotency class	2
isoclinism	isoclinic class of #120
automorphism	?
homology	Abelianization (H₁) = C₂⁶×C₅ · Schur multiplier (H₂) = C₂¹⁴

Aliases

C₂³×C₅×C₂²⋊Q₈

	subgroup	G/H
center, socle	C₂⁵×C₅	C₂³
commutator, Frattini, cosocle	C₂²	C₂⁶×C₅
prime radical	C₂⁶×C₅	C₂²
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂⁵×C₅ ◁ G

14078 conjugacy classes of subgroups.

minimal degree	μ(G) = 23
transitive degree	μ_t(G) = 640

A minimal faithful permutation representation — 6 generators on 23 points:

(1,2)(19,20,21,22,23);(3,4);(5,6);(8,10)(11,12,14,16)(13,17,18,15);(11,13,14,18)(12,15,16,17);(7,8)(9,10)(11,12)(13,15)(14,16)(17,18)

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1280, 55645);