C₂₅×#479 #13098628

order	1600
nilpotency class	3
isoclinism	isoclinic class of #447
automorphism	?
homology	Abelianization (H₁) = C₂³×C₂₅ · Schur multiplier (H₂) = C₂

Aliases

direct product

C₂₅×#479

Subgroups

	subgroup	G/H
center	C₂²×C₂₅	C₂×D₄
commutator	C₂×C₄	C₂³×C₂₅
Frattini, cosocle	C₂×C₄×C₅	C₂³×C₅
socle, prime radical	C₂²×C₅	C₂×C₅×D₄
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₂₅ ◁ C₄²×C₂₅ ◁ G

135 conjugacy classes of subgroups; only the 81 normal subgroups are shown.

normal subgroups only

This group has 135 conjugacy classes of subgroups — too many to draw. Only its 81 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) = 49
transitive degree	μ_t(G) = 1600

A minimal faithful permutation representation — 3 generators on 49 points:

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

Conjugacy classes & character table

475 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1600, 980);