C₂×C₅×D₁₉×C₅₃ #34117821

order	20140
isoclinism	isoclinic class of D₁₉
automorphism	?
homology	Abelianization (H₁) = C₂²×C₅×C₅₃ · Schur multiplier (H₂) = C₂

Aliases

direct product	C₂×C₅×D₁₉×C₅₃
unambiguous semidirect product	C₁₉⋊(C₂²×C₅×C₅₃)
unambiguous semidirect product	(C₂×C₁₉)⋊(C₂×C₅×C₅₃)

Splittings

Fitting, socle	C₂×C₅×C₁₉×C₅₃ ⋊ C₂
derived, Sylow	C₁₉ ⋊ C₂²×C₅×C₅₃
Hall	C₅×C₁₉×C₅₃ ⋊ C₂²
Hall	C₁₉×C₅₃ ⋊ C₂²×C₅
Hall	C₅×C₁₉ ⋊ C₂²×C₅₃

Subgroups

	subgroup	G/H
center, hypercenter	C₂×C₅×C₅₃	D₁₉
commutator, cosocle, hypocenter	C₁₉	C₂²×C₅×C₅₃
Frattini	C₁	G
Fitting, socle	C₂×C₅×C₁₉×C₅₃	C₂
LCS	G ▷ C₁₉
UCS	C₁ ◁ C₂×C₅×C₅₃

40 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 79
transitive degree	μ_t(G) = 10070

A minimal faithful permutation representation — 2 generators on 79 points:

(2,3)(4,5)(6,7)(8,9)(10,11)(12,13)(14,15)(16,17)(18,19)(20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72)(73,74,75,76,77);(1,2,4,6,8,10,12,14,16,18,19,17,15,13,11,9,7,5,3)(78,79)

Conjugacy classes & character table

5830 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(20140, 30);

C2×C5×D19×C53 #34117821