C₅²×D₄₁ #14523320

order	2050
isoclinism	isoclinic class of D₄₁
automorphism	?
homology	Abelianization (H₁) = C₂×C₅² · Schur multiplier (H₂) = C₅

Aliases

direct product

C₅²×D₄₁

Splittings

Fitting, socle, Hall	C₅²×C₄₁ ⋊ C₂
derived, Sylow	C₄₁ ⋊ C₂×C₅²

Subgroups

	subgroup	G/H
center, hypercenter	C₅²	D₄₁
commutator, cosocle, hypocenter	C₄₁	C₂×C₅²
Frattini	C₁	G
Fitting, socle	C₅²×C₄₁	C₂
LCS	G ▷ C₄₁
UCS	C₁ ◁ C₅²

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 51
transitive degree	μ_t(G) = 1025

A minimal faithful permutation representation — 2 generators on 51 points:

(1,2,3,4,5)(11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51);(6,7,8,9,10)(12,51)(13,50)(14,49)(15,48)(16,47)(17,46)(18,45)(19,44)(20,43)(21,42)(22,41)(23,40)(24,39)(25,38)(26,37)(27,36)(28,35)(29,34)(30,33)(31,32)

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₅²×#4223, C₅×#11717964, C₅×D₅×D₄₁, …
maximal normal subgroup of	C₅²×#4223, C₅×#11717964, C₅×D₅×D₄₁, …
maximal quotient of	C₅²×Dic₄₁, C₂×C₅²×D₄₁, C₅²×D₂₈₇, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2050, 12);

C52×D41 #14523320