C₂×C₅×C₃⋊(C₁₉⋊D₁₉) #36343290

order	21660
automorphism	?
homology	Abelianization (H₁) = C₂²×C₅ · Schur multiplier (H₂) = C₂×C₁₉

Aliases

direct product	C₂×C₅×C₃⋊(C₁₉⋊D₁₉)
unambiguous semidirect product	(C₂×C₃)⋊(C₅×C₁₉⋊D₁₉)
unambiguous semidirect product	(C₂×C₁₉)⋊(C₅×D₅₇)

Splittings

Fitting, socle	C₂×C₃×C₅×C₁₉² ⋊ C₂
derived, Hall	C₃×C₁₉² ⋊ C₂²×C₅
Hall	C₃×C₅×C₁₉² ⋊ C₂²
Hall	C₅×C₁₉² ⋊ C₂×D₃
Sylow	C₁₉² ⋊ C₂×C₅×D₃
Hall	C₃×C₅ ⋊ C₂×C₁₉⋊D₁₉
Sylow	C₃ ⋊ C₂×C₅×C₁₉⋊D₁₉

Subgroups

	subgroup	G/H
center, hypercenter	C₂×C₅	C₃⋊(C₁₉⋊D₁₉)
commutator, cosocle, hypocenter	C₃×C₁₉²	C₂²×C₅
Frattini	C₁	G
Fitting, socle	C₂×C₃×C₅×C₁₉²	C₂
LCS	G ▷ C₃×C₁₉²
UCS	C₁ ◁ C₂×C₅

440 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 48
transitive degree	μ_t(G) = 10830

A minimal faithful permutation representation — 3 generators on 48 points:

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

Conjugacy classes & character table

5430 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(21660, 214);

C2×C5×C3⋊(C19⋊D19) #36343290