C₅×D₃×C₄₃ #13046262

order	1290
isoclinism	isoclinic class of D₃
automorphism	?
homology	Abelianization (H₁) = C₂×C₅×C₄₃ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₅×D₃×C₄₃
unambiguous semidirect product	C₃⋊(C₂×C₅×C₄₃)

Splittings

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

Subgroups

	subgroup	G/H
center, hypercenter	C₅×C₄₃	D₃
commutator, cosocle, hypocenter	C₃	C₂×C₅×C₄₃
Frattini	C₁	G
Fitting, socle	C₃×C₅×C₄₃	C₂
LCS	G ▷ C₃
UCS	C₁ ◁ C₅×C₄₃

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);(7,8)

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₅×D₃×D₄₃, D₃×D₅×C₄₃, D₃×D₂₁₅, …
maximal normal subgroup of	C₅×D₃×D₄₃, D₃×D₅×C₄₃, D₃×D₂₁₅, …
maximal quotient of	C₅×Dic₃×C₄₃, C₂×C₅×D₃×C₄₃, C₅×D₉×C₄₃, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1290, 8);

C5×D3×C43 #13046262