C₃×C₅×D₄₃ #13046259

order	1290
isoclinism	isoclinic class of D₄₃
automorphism	?
homology	Abelianization (H₁) = C₂×C₃×C₅ · Schur multiplier (H₂) = C₁

Aliases

direct product

C₃×C₅×D₄₃

Splittings

Fitting, socle, Hall	C₃×C₅×C₄₃ ⋊ C₂
derived, Sylow	C₄₃ ⋊ C₂×C₃×C₅
Hall	C₅×C₄₃ ⋊ C₂×C₃
Hall	C₃×C₄₃ ⋊ C₂×C₅

Subgroups

	subgroup	G/H
center, hypercenter	C₃×C₅	D₄₃
commutator, cosocle, hypocenter	C₄₃	C₂×C₃×C₅
Frattini	C₁	G
Fitting, socle	C₃×C₅×C₄₃	C₂
LCS	G ▷ C₄₃
UCS	C₁ ◁ C₃×C₅

16 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 51
transitive degree	μ_t(G) = 645

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

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

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₃×D₅×D₄₃, C₅×D₃×D₄₃, D₁₅×D₄₃, …
maximal normal subgroup of	C₃×D₅×D₄₃, C₅×D₃×D₄₃, D₁₅×D₄₃, …
maximal quotient of	C₃×C₅×Dic₄₃, C₂×C₃×C₅×D₄₃, C₅×C₉×D₄₃, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1290, 5);

C3×C5×D43 #13046259