C₂×#31772345 #46829313

order	34596
automorphism	?
homology	Abelianization (H₁) = C₂²×C₉ · Schur multiplier (H₂) = C₂×C₃₁

Aliases

direct product

C₂×#31772345

Splittings

derived, Sylow	C₃₁² ⋊ C₂²×C₉
Hall	#22575711 ⋊ C₂²
Hall	C₂×C₃₁⋊D₃₁ ⋊ C₉

Subgroups

	subgroup	G/H
center, hypercenter	C₂×C₃	#19153444
commutator, hypocenter	C₃₁²	C₂²×C₉
Frattini	C₃	C₂×#19153444
Fitting, socle	C₂×C₃×C₃₁²	C₂×C₃
prime radical	C₂×C₃×C₃₁⋊D₃₁	C₃
cosocle	C₃×C₃₁²	C₂²×C₃
LCS	G ▷ C₃₁²
UCS	C₁ ◁ C₂×C₃

160 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 73
transitive degree	μ_t(G) = 558

A minimal faithful permutation representation — 2 generators on 73 points:

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

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(34596, 73);

C2×#31772345 #46829313