C₁₉×AGL(1,𝔽₅)×C₅₃ #34117804

order	20140
isoclinism	isoclinic class of AGL(1,𝔽₅)
automorphism	?
homology	Abelianization (H₁) = C₄×C₁₉×C₅₃ · Schur multiplier (H₂) = C₁

Aliases

direct product

C₁₉×AGL(1,𝔽₅)×C₅₃

Splittings

Fitting, socle, Hall	C₅×C₁₉×C₅₃ ⋊ C₄
derived, Sylow	C₅ ⋊ C₄×C₁₉×C₅₃
Hall	C₅×C₅₃ ⋊ C₄×C₁₉
Hall	C₅×C₁₉ ⋊ C₄×C₅₃

Subgroups

	subgroup	G/H
center, hypercenter	C₁₉×C₅₃	AGL(1,𝔽₅)
commutator, hypocenter	C₅	C₄×C₁₉×C₅₃
Frattini	C₁	G
Fitting, socle	C₅×C₁₉×C₅₃	C₄
prime radical	D₅×C₁₉×C₅₃	C₂
cosocle	D₅	C₂×C₁₉×C₅₃
LCS	G ▷ C₅
UCS	C₁ ◁ C₁₉×C₅₃

24 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 77
transitive degree	μ_t(G) = 5035

A minimal faithful permutation representation — 2 generators on 77 points:

(2,5,4,3)(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);(1,2,3,5,4)

Conjugacy classes & character table

5035 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(20140, 13);

C19×AGL(1,𝔽5)×C53 #34117804