C₅×#10534 #11933254

order	1280
nilpotency class	3
isoclinism	isoclinic class of #10530
automorphism	?
homology	Abelianization (H₁) = C₂³×C₅ · Schur multiplier (H₂) = C₂²

Aliases

direct product

C₅×#10534

Subgroups

	subgroup	G/H
center, socle	C₂²×C₅	#394
commutator, Frattini, cosocle	C₂×C₄²	C₂³×C₅
prime radical	C₂³×C₅	#124
LCS	G ▷ C₂×C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₅ ◁ C₂×C₄²×C₅ ◁ G

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

normal subgroups only

This group has 358 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) = 29
transitive degree	μ_t(G) = 640

A minimal faithful permutation representation — 3 generators on 29 points:

(1,2,3,4,5)(6,7)(8,11)(9,12)(10,13)(14,15,19,23)(16,24,26,29)(17,21,25,20)(18,28,27,22);(6,7)(8,12)(9,11)(10,13)(14,16,19,26)(15,20,23,21)(17,27,25,18)(22,29,28,24);(7,11)(8,9)(12,13)(14,17,18,16,19,25,27,26)(15,21,22,29,23,20,28,24)

Conjugacy classes & character table

170 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1280, 3522);