D₅₃×#1829 #27383952

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

Aliases

direct product

D₅₃×#1829

Splittings

Fitting	C₅₃×#1829 ⋊ C₂
Sylow	C₅₃ ⋊ C₂×#1829

Subgroups

	subgroup	G/H
center	C₂	#381×D₅₃
commutator	C₂³×C₅₃	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₅₃
Fitting	C₅₃×#1829	C₂
socle	C₂×C₅₃	C₂×#381
prime radical	C₂²×D₄×D₅₃	C₂²
cosocle	C₂²×C₄×C₅₃	C₂⁴
hypercenter	#1829	D₅₃
hypocenter	C₅₃	C₂×#1829
LCS	G ▷ C₂³×C₅₃ ▷ C₂×C₅₃ ▷ C₅₃
UCS	C₁ ◁ C₂ ◁ C₂²×C₄ ◁ #1829

1434 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)(54,56)(55,60,59,62)(57,64)(58,63)(61,68,66,69)(65,67);(55,59)(57,65)(60,62)(64,67);(54,55,57,61,58,59,65,66)(56,62,64,69,63,60,67,68);(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, 169428);

D53×#1829 #27383952