C₃×C₅⋊#14524206 #44570590

order	32490
automorphism	?
homology	Abelianization (H₁) = C₂×C₃² · Schur multiplier (H₂) = C₃

Aliases

direct product	C₃×C₅⋊#14524206
unambiguous semidirect product	C₅⋊(C₃×#14524206)

Splittings

Fitting, socle	C₃×C₅×C₁₉² ⋊ C₂×C₃
derived, Hall	C₅×C₁₉² ⋊ C₂×C₃²
Hall	C₃×C₅×#11762245 ⋊ C₂
Hall	C₅⋊(C₁₉⋊D₁₉) ⋊ C₃²
Hall	C₃×#11762245 ⋊ D₅
Sylow	C₁₉² ⋊ C₃²×D₅
Sylow	C₅ ⋊ C₃×#14524206

Subgroups

	subgroup	G/H
center, hypercenter	C₃	C₅⋊#14524206
commutator, cosocle, hypocenter	C₅×C₁₉²	C₂×C₃²
Frattini	C₁	G
Fitting, socle	C₃×C₅×C₁₉²	C₂×C₃
LCS	G ▷ C₅×C₁₉²
UCS	C₁ ◁ C₃

528 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 46
transitive degree	μ_t(G) = 5415

A minimal faithful permutation representation — 3 generators on 46 points:

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

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(32490, 174);

C3×C5⋊#14524206 #44570590