C₂₅×#520 #13099173

order	1600
nilpotency class	2
isoclinism	isoclinic class of H(5,𝔽₂)
automorphism	?
homology	Abelianization (H₁) = C₂³×C₄×C₂₅ · Schur multiplier (H₂) = C₂⁵

Aliases

direct product

C₂₅×#520

Subgroups

	subgroup	G/H
center	C₂²×C₂₅	C₂⁴
commutator	C₂	C₂³×C₄×C₂₅
Frattini, socle, cosocle	C₂²×C₅	C₂⁴×C₅
prime radical	C₂×C₅×#41	C₂×C₅
LCS	G ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₂₅ ◁ G

441 conjugacy classes of subgroups; only the 363 normal subgroups are shown.

normal subgroups only

This group has 441 conjugacy classes of subgroups — too many to draw. Only its 363 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) = 37
transitive degree	μ_t(G) = 800

A minimal faithful permutation representation — 4 generators on 37 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)(32,36)(33,34)(35,37);(31,34)(35,36);(30,31)(32,35)(33,34)(36,37);(30,32,33,37)(31,35,34,36)

Conjugacy classes & character table

850 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1600, 1525);