C₅×#12173 #11934893

order	1280
nilpotency class	4
isoclinism	isoclinic class of #12173
automorphism	?
homology	Abelianization (H₁) = C₂³×C₅ · Schur multiplier (H₂) = C₂³

Aliases

	subgroup	G/H
center, socle	C₂×C₅	#1598
commutator, Frattini, cosocle	C₂×M₁₆	C₂³×C₅
LCS	G ▷ C₂×M₁₆ ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₅ ◁ C₂×C₄×C₅ ◁ C₂×C₅×M₁₆ ◁ G

384 conjugacy classes of subgroups; only the 70 normal subgroups are shown.

normal subgroups only

This group has 384 conjugacy classes of subgroups — too many to draw. Only its 70 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

minimal degree	μ(G) = 21
transitive degree	μ_t(G) = 80

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

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1280, 5161);