D₅₃×#1913 #27386099

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

Aliases

direct product

D₅₃×#1913

Splittings

Fitting	C₅₃×#1913 ⋊ C₂
Sylow	C₅₃ ⋊ C₂×#1913

Subgroups

	subgroup	G/H
center	C₂	#386×D₅₃
commutator	C₂³×C₅₃	C₂³×C₄
Frattini	C₂⁴	C₂³×D₅₃
Fitting	C₅₃×#1913	C₂
socle	C₂×C₅₃	C₂×#386
prime radical	#534×D₅₃	C₂
cosocle	C₂⁴×C₅₃	C₂⁴
hypercenter	#1913	D₅₃
hypocenter	C₅₃	C₂×#1913
LCS	G ▷ C₂³×C₅₃ ▷ C₂×C₅₃ ▷ C₅₃
UCS	C₁ ◁ C₂ ◁ C₂⁴ ◁ #1913

2078 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)(56,62)(58,65)(59,66)(61,64)(63,68)(67,69);(54,56)(55,59,61,67)(57,62)(58,63)(60,66,64,69)(65,68);(54,55)(56,59,63,67)(57,64,65,60)(58,61)(62,66)(68,69);(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, 171575);

D53×#1913 #27386099