D₅₃×#1979 #27388088

order	13568
automorphism	?
homology	Abelianization (H₁) = C₂³×C₄ · Schur multiplier (H₂) = C₂⁵×C₄

Aliases

direct product

D₅₃×#1979

Splittings

Fitting	C₅₃×#1979 ⋊ C₂
Sylow	C₅₃ ⋊ C₂×#1979

Subgroups

	subgroup	G/H
center	C₂²	#121×D₅₃
commutator	C₂×C₄×C₅₃	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₅₃
Fitting	C₅₃×#1979	C₂
socle	C₂²×C₅₃	C₂×#121
prime radical	C₂³×D₅₃	#41
cosocle	C₂²×C₄×C₅₃	C₂⁴
hypercenter	#1979	D₅₃
hypocenter	C₅₃	C₂×#1979
LCS	G ▷ C₂×C₄×C₅₃ ▷ C₂×C₅₃ ▷ C₅₃
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ #1979

1438 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 89
transitive degree	μ_t(G) = 3392

A minimal faithful permutation representation — 4 generators on 89 points:

(5,8,10,21,11,22,9,20)(6,13,23,33,14,29,15,19)(7,16,24,34,17,31,18,32)(12,25,27,35,28,36,26,30)(37,38,40,42,44,46,48,50,52,54,56,58,60,62,64,66,68,70,72,74,76,78,80,82,84,86,88,89,87,85,83,81,79,77,75,73,71,69,67,65,63,61,59,57,55,53,51,49,47,45,43,41,39);(1,3,4,2)(5,7,9,18,11,17,10,24)(6,12,15,26,14,28,23,27)(8,16,20,32,22,31,21,34)(13,25,19,30,29,36,33,35);(1,2,4,3)(5,6,10,15,11,14,9,23)(7,12,18,27,17,28,24,26)(8,19,21,29,22,33,20,13)(16,30,32,25,31,35,34,36);(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)(78,79)(80,81)(82,83)(84,85)(86,87)(88,89)

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13568, 173564);

D53×#1979 #27388088