C₅²×D₃₁ #13095465

order	1550
isoclinism	isoclinic class of D₃₁
automorphism	?
homology	Abelianization (H₁) = C₂×C₅² · Schur multiplier (H₂) = C₅

Aliases

direct product

C₅²×D₃₁

Splittings

Fitting, socle, Hall	C₅²×C₃₁ ⋊ C₂
derived, Sylow	C₃₁ ⋊ C₂×C₅²

Subgroups

	subgroup	G/H
center, hypercenter	C₅²	D₃₁
commutator, cosocle, hypocenter	C₃₁	C₂×C₅²
Frattini	C₁	G
Fitting, socle	C₅²×C₃₁	C₂
LCS	G ▷ C₃₁
UCS	C₁ ◁ C₅²

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 41
transitive degree	μ_t(G) = 775

A minimal faithful permutation representation — 2 generators on 41 points:

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

Conjugacy classes & character table

425 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₅×D₅×D₃₁, C₅⋊D₅×D₃₁, C₂×C₅²×D₃₁, …
maximal normal subgroup of	C₅×D₅×D₃₁, C₅⋊D₅×D₃₁, C₂×C₅²×D₃₁, …
maximal quotient of	C₅²×Dic₃₁, C₂×C₅²×D₃₁, C₃×C₅²×D₃₁, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1550, 11);

C52×D31 #13095465