D₅₃×#1914 #27386111

order	13568
automorphism	?
homology	Abelianization (H₁) = C₂³×C₄ · Schur multiplier (H₂) = C₂⁷

Aliases

direct product

D₅₃×#1914

Splittings

Fitting	C₅₃×#1914 ⋊ C₂
Sylow	C₅₃ ⋊ C₂×#1914

Subgroups

	subgroup	G/H
center	C₂	#386×D₅₃
commutator	C₂³×C₅₃	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₅₃
Fitting	C₅₃×#1914	C₂
socle	C₂×C₅₃	C₂×#386
prime radical	#535×D₅₃	C₂
cosocle	C₂²×C₄×C₅₃	C₂⁴
hypercenter	#1914	D₅₃
hypocenter	C₅₃	C₂×#1914
LCS	G ▷ C₂³×C₅₃ ▷ C₂×C₅₃ ▷ C₅₃
UCS	C₁ ◁ C₂ ◁ C₂²×C₄ ◁ #1914

1862 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 69
transitive degree	μ_t(G) = 848

A minimal faithful permutation representation — 4 generators on 69 points:

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

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13568, 171587);

D53×#1914 #27386111