D₅₃×#2614 #27551002

order	13568
automorphism	?
homology	Abelianization (H₁) = C₂⁵ · Schur multiplier (H₂) = C₂¹⁰

Aliases

direct product

D₅₃×#2614

Splittings

Fitting	C₅₃×#2614 ⋊ C₂
Sylow	C₅₃ ⋊ C₂×#2614

Subgroups

	subgroup	G/H
center, Frattini	C₂³	C₂⁴×D₅₃
commutator, socle, cosocle	C₂³×C₅₃	C₂⁵
Fitting	C₅₃×#2614	C₂
prime radical	C₂²×D₄×D₅₃	C₂²
hypercenter	#2614	D₅₃
hypocenter	C₅₃	C₂×#2614
LCS	G ▷ C₂³×C₅₃ ▷ C₅₃
UCS	C₁ ◁ C₂³ ◁ #2614

5194 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 77
transitive degree	μ_t(G) = 3392

A minimal faithful permutation representation — 5 generators on 77 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)(65,73)(68,75)(71,77)(74,76);(55,57)(59,61)(62,65)(63,68)(64,71)(66,73)(67,74)(69,75)(70,76)(72,77);(58,59)(60,61)(62,64,66,72)(63,67,69,70)(65,71,73,77)(68,74,75,76);(54,55)(56,57)(62,63,66,69)(64,70,72,67)(65,68,73,75)(71,76,77,74);(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

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13568, 336478);

D53×#2614 #27551002