C₅²×D₂₉ #13089695

order	1450
isoclinism	isoclinic class of D₂₉
automorphism	?
homology	Abelianization (H₁) = C₂×C₅² · Schur multiplier (H₂) = C₅

Aliases

direct product	C₅²×D₂₉
unambiguous semidirect product	C₂₉⋊(C₂×C₅²)

Splittings

Fitting, socle, Hall	C₅²×C₂₉ ⋊ C₂
derived, Sylow	C₂₉ ⋊ C₂×C₅²

Subgroups

	subgroup	G/H
center, hypercenter	C₅²	D₂₉
commutator, cosocle, hypocenter	C₂₉	C₂×C₅²
Frattini	C₁	G
Fitting, socle	C₅²×C₂₉	C₂
LCS	G ▷ C₂₉
UCS	C₁ ◁ C₅²

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 39
transitive degree	μ_t(G) = 725

A minimal faithful permutation representation — 2 generators on 39 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);(6,7,8,9,10)(12,39)(13,38)(14,37)(15,36)(16,35)(17,34)(18,33)(19,32)(20,31)(21,30)(22,29)(23,28)(24,27)(25,26)

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₅²×#1181, C₅×#10596817, C₅×D₅×D₂₉, …
maximal normal subgroup of	C₅²×#1181, C₅×#10596817, C₅×D₅×D₂₉, …
maximal quotient of	C₅²×Dic₂₉, C₂×C₅²×D₂₉, C₃×C₅²×D₂₉, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1450, 5);

C52×D29 #13089695