C₅×#13660 #11936380

order	1280
nilpotency class	2
isoclinism	isoclinic class of #120
automorphism	?
homology	Abelianization (H₁) = C₂²×C₅×C₁₆ · Schur multiplier (H₂) = C₂

Aliases

direct product

C₅×#13660

Subgroups

	subgroup	G/H
center	C₂×C₅×C₁₆	C₂³
commutator	C₂²	C₂²×C₅×C₁₆
Frattini, cosocle	C₂×C₁₆	C₂³×C₅
socle, prime radical	C₂²×C₅	C₂²×C₁₆
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂×C₅×C₁₆ ◁ G

158 conjugacy classes of subgroups; only the 126 normal subgroups are shown.

normal subgroups only

This group has 158 conjugacy classes of subgroups — too many to draw. Only its 126 normal subgroups are shown.

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

Full subgroup data →

Presentation

minimal degree	μ(G) = 45
transitive degree	μ_t(G) = 1280

A minimal faithful permutation representation — 3 generators on 45 points:

(1,2,3,4,5)(6,7)(8,13)(9,11)(10,12)(14,15,17,22,18,23,29,37,19,16,25,26,31,27,40,41,20,24,30,38,32,39,43,45,33,28,21,34,35,42,36,44);(6,8,10,9)(7,11,12,13);(6,9,10,8)(7,11,12,13)(14,16,17,26,18,27,29,41,19,24,25,38,31,39,40,45,20,28,30,34,32,42,43,44,33,15,21,22,35,23,36,37)

Conjugacy classes & character table

560 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1280, 6648);