C₂₅×#467 #13098616

order	1600
nilpotency class	3
isoclinism	isoclinic class of #465
automorphism	?
homology	Abelianization (H₁) = C₂³×C₂₅ · Schur multiplier (H₂) = C₂²

Aliases

direct product

C₂₅×#467

Subgroups

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

171 conjugacy classes of subgroups; only the 87 normal subgroups are shown.

normal subgroups only

This group has 171 conjugacy classes of subgroups — too many to draw. Only its 87 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) = 800

A minimal faithful permutation representation — 3 generators on 45 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)(28,29)(30,31,34,37)(32,38,41,45)(33,42,39,36)(35,43,44,40);(30,32,39,43,34,41,33,40)(31,35,42,45,37,44,36,38);(27,29)

Conjugacy classes & character table

550 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1600, 968);