C₅×#7479 #11930199

order	1280
nilpotency class	5
isoclinism	isoclinic class of #1418
automorphism	?
homology	Abelianization (H₁) = C₄²×C₅ · Schur multiplier (H₂) = C₂²

Aliases

direct product

C₅×#7479

Subgroups

	subgroup	G/H
center	C₄×C₅	#357
commutator	C₁₆	C₄²×C₅
Frattini, cosocle	C₂²×C₁₆	C₂²×C₅
socle	C₂×C₅	#1380
prime radical	C₂³×C₅	Q₃₂
LCS	G ▷ C₁₆ ▷ C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₄×C₅ ◁ C₂²×C₄×C₅ ◁ C₂²×C₅×C₈ ◁ C₂²×C₅×C₁₆ ◁ G

162 conjugacy classes of subgroups; only the 98 normal subgroups are shown.

normal subgroups only

This group has 162 conjugacy classes of subgroups — too many to draw. Only its 98 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) = 69
transitive degree	μ_t(G) = 320

A minimal faithful permutation representation — 2 generators on 69 points:

(1,2,3,4,5)(6,7,10,16,13,20,33,19)(8,21,23,53,26,44,58,54)(9,27,30,50,31,17,34,48)(11,15,32,45,35,47,66,46)(12,36,29,18,37,49,65,51)(14,38,39,28,43,64,42,22)(24,59,57,69,56,52,67,41)(25,60,55,40,61,68,63,62);(6,8,11,24,12,25,34,38,33,58,66,67,65,63,31,22,13,26,35,56,37,61,30,64,10,23,32,57,29,55,9,28)(7,14,17,40,18,41,46,53,16,39,48,68,49,59,15,44,20,43,27,62,51,69,45,54,19,42,50,60,36,52,47,21)

Conjugacy classes & character table

260 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1280, 467);