C₂₅×#394 #13098543

order	1600
nilpotency class	2
isoclinism	isoclinic class of #392
automorphism	?
homology	Abelianization (H₁) = C₂³×C₂₅ · Schur multiplier (H₂) = C₂⁴

Aliases

direct product

C₂₅×#394

Subgroups

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

357 conjugacy classes of subgroups; only the 117 normal subgroups are shown.

normal subgroups only

This group has 357 conjugacy classes of subgroups — too many to draw. Only its 117 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 — 3 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)(31,33)(34,35)(36,37);(27,29)(31,33)(35,36);(26,27)(28,29)(30,31)(32,33)(34,36,37,35)

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, 895);