D₅₃×#2028 #27411454

order	13568
automorphism	?
homology	Abelianization (H₁) = C₂⁴ · Schur multiplier (H₂) = C₂⁶

Aliases

direct product

D₅₃×#2028

Splittings

Fitting	C₅₃×#2028 ⋊ C₂
Sylow	C₅₃ ⋊ C₂×#2028

Subgroups

	subgroup	G/H
center	C₂²	#120×D₅₃
commutator, cosocle	C₂²×C₄×C₅₃	C₂⁴
Frattini	C₂²×C₄	C₂³×D₅₃
Fitting	C₅₃×#2028	C₂
socle	C₂²×C₅₃	C₂×#120
prime radical	C₂³×D₅₃	C₂×D₄
hypercenter	#2028	D₅₃
hypocenter	C₅₃	C₂×#2028
LCS	G ▷ C₂²×C₄×C₅₃ ▷ C₂×C₅₃ ▷ C₅₃
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ #2028

1238 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 77
transitive degree	μ_t(G) = 1696

A minimal faithful permutation representation — 4 generators on 77 points:

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

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13568, 196930);

D53×#2028 #27411454