C₅×#9979 #11932699

order	1280
nilpotency class	3
isoclinism	isoclinic class of #9974
automorphism	?
homology	Abelianization (H₁) = C₂³×C₅ · Schur multiplier (H₂) = C₂³

Aliases

direct product

C₅×#9979

Subgroups

	subgroup	G/H
center, socle	C₂²×C₅	#392
commutator, Frattini, cosocle	C₂³×C₄	C₂³×C₅
prime radical	C₂⁴×C₅	#41
LCS	G ▷ C₂³×C₄ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₅ ◁ C₂³×C₄×C₅ ◁ G

492 conjugacy classes of subgroups; only the 102 normal subgroups are shown.

normal subgroups only

This group has 492 conjugacy classes of subgroups — too many to draw. Only its 102 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) = 53
transitive degree	μ_t(G) = 320

A minimal faithful permutation representation — 3 generators on 53 points:

(1,2,3,4,5)(6,7)(8,11)(9,12)(10,13)(14,17)(15,18)(16,20)(19,21)(22,23,28,32)(24,33,37,45)(25,38,42,48)(26,43,27,31)(29,36,46,35)(30,40,49,41)(34,51,52,44)(39,50,53,47);(6,8,10,15)(7,11,13,18)(9,14,16,21)(12,19,20,17)(22,24)(23,29)(25,39)(26,36)(27,35)(28,37)(30,47)(31,45)(32,46)(33,43)(34,40)(38,44)(41,52)(42,53)(48,51)(49,50);(6,9)(7,12)(8,14)(10,16)(11,17)(13,20)(15,21)(18,19)(22,25,28,42)(23,30,32,49)(24,34,37,52)(26,40,27,41)(29,44,46,51)(31,48,43,38)(33,50,45,47)(35,39,36,53)

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, 2967);