D₅₃×#1910 #27386067

order	13568
automorphism	?
homology	Abelianization (H₁) = C₂³×C₄ · Schur multiplier (H₂) = C₂⁶×C₄

Aliases

direct product

D₅₃×#1910

Splittings

Fitting	C₅₃×#1910 ⋊ C₂
Sylow	C₅₃ ⋊ C₂×#1910

Subgroups

	subgroup	G/H
center	C₂	#386×D₅₃
commutator	C₂×C₄×C₅₃	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₅₃
Fitting	C₅₃×#1910	C₂
socle	C₂×C₅₃	C₂×#386
prime radical	#535×D₅₃	C₂
cosocle	C₂²×C₄×C₅₃	C₂⁴
hypercenter	#1910	D₅₃
hypocenter	C₅₃	C₂×#1910
LCS	G ▷ C₂×C₄×C₅₃ ▷ C₂×C₅₃ ▷ C₅₃
UCS	C₁ ◁ C₂ ◁ C₂²×C₄ ◁ #1910

1878 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:

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

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, 171543);

D53×#1910 #27386067