D₅₃×#2274 #27542298

order	13568
automorphism	?
homology	Abelianization (H₁) = C₂³×C₄² · Schur multiplier (H₂) = C₂⁸×C₄

Aliases

direct product

D₅₃×#2274

Splittings

Fitting	C₅₃×#2274 ⋊ C₂
Sylow	C₅₃ ⋊ C₂×#2274

Subgroups

	subgroup	G/H
center, Frattini	C₂³	C₂⁴×D₅₃
commutator	C₂×C₅₃	C₂³×C₄²
Fitting	C₅₃×#2274	C₂
socle, cosocle	C₂³×C₅₃	C₂⁵
prime radical	C₂⁴×D₅₃	C₂³
hypercenter	#2274	D₅₃
hypocenter	C₅₃	C₂×#2274
LCS	G ▷ C₂×C₅₃ ▷ C₅₃
UCS	C₁ ◁ C₂³ ◁ #2274

4110 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 69
transitive degree	μ_t(G) = 3392

A minimal faithful permutation representation — 5 generators on 69 points:

(10,13)(14,16)(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);(9,11,12,15)(10,14,13,16);(5,6,7,8)(10,13)(11,15);(1,2,3,4)(9,10)(11,14)(12,13)(15,16);(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

1904 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13568, 327774);

D53×#2274 #27542298