D₅×#16809824 #46776713

order	33550
automorphism	?
homology	Abelianization (H₁) = C₂×C₅ · Schur multiplier (H₂) = C₁

Aliases

direct product	D₅×#16809824
unambiguous semidirect product	C₅⋊(C₂×#16809824)

Splittings

Fitting, socle, derived	C₅×C₁₁×C₆₁ ⋊ C₂×C₅
Hall	C₅×#16809824 ⋊ C₂
Hall	C₁₁×C₆₁ ⋊ C₅×D₅
Sylow	C₆₁ ⋊ D₅×C₁₁⋊C₅
Sylow	C₁₁ ⋊ D₅×C₆₁⋊C₅

Subgroups

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₅×C₁₁×C₆₁	C₂×C₅
LCS	G ▷ C₅×C₁₁×C₆₁
UCS	C₁

40 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 77
transitive degree	μ_t(G) = 3355

A minimal faithful permutation representation — 2 generators on 77 points:

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

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(33550, 73);

D5×#16809824 #46776713