C₂₅×#432 #13098581

order	1600
nilpotency class	2
isoclinism	isoclinic class of #120
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₂₅ · Schur multiplier (H₂) = C₂²

Aliases

direct product

C₂₅×#432

Subgroups

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

165 conjugacy classes of subgroups; only the 111 normal subgroups are shown.

normal subgroups only

This group has 165 conjugacy classes of subgroups — too many to draw. Only its 111 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) = 41
transitive degree	μ_t(G) = 800

A minimal faithful permutation representation — 3 generators on 41 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)(28,31)(29,30)(32,33)(34,35,36,39,37,38,40,41);(27,30)(31,33);(26,28,29,32)(27,31,30,33)(35,38)(39,41)

Conjugacy classes & character table

700 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1600, 933);