C₂×C₂₅×#101 #13098561

order	1600
nilpotency class	3
isoclinism	isoclinic class of #99
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₂₅ · Schur multiplier (H₂) = C₂³

Aliases

direct product

C₂×C₂₅×#101

Subgroups

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

219 conjugacy classes of subgroups; only the 123 normal subgroups are shown.

normal subgroups only

This group has 219 conjugacy classes of subgroups — too many to draw. Only its 123 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) = 43
transitive degree	μ_t(G) = 800

A minimal faithful permutation representation — 3 generators on 43 points:

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

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, 913);