D₄₇×#3127 #27084627

order	12032
automorphism	?
homology	Abelianization (H₁) = C₂⁵ · Schur multiplier (H₂) = C₂⁸

Aliases

direct product

D₄₇×#3127

Splittings

Fitting	C₄₇×#3127 ⋊ C₂
Sylow	C₄₇ ⋊ C₂×#3127

Subgroups

	subgroup	G/H
center	C₂²	C₂²×D₄×D₄₇
commutator, cosocle	C₂×C₄×C₄₇	C₂⁵
Frattini	C₂×C₄	C₂⁴×D₄₇
Fitting	C₄₇×#3127	C₂
socle	C₂²×C₄₇	C₂³×D₄
prime radical	C₂³×D₄₇	C₂×D₄
hypercenter	#3127	D₄₇
hypocenter	C₄₇	C₂×#3127
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂² ◁ #117 ◁ #3127

1994 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 87
transitive degree	μ_t(G) = 3008

A minimal faithful permutation representation — 5 generators on 87 points:

(1,3,4,7)(2,6,5,8)(11,21)(15,19)(20,36)(22,38)(29,33)(30,34)(35,40)(37,39)(41,42,44,46,48,50,52,54,56,58,60,62,64,66,68,70,72,74,76,78,80,82,84,86,87,85,83,81,79,77,75,73,71,69,67,65,63,61,59,57,55,53,51,49,47,45,43);(9,12,13,24)(10,16,17,31)(11,20,21,36)(14,28,26,25)(15,29,19,33)(18,32,27,23)(22,39,38,37)(30,35,34,40);(2,5)(6,8)(9,11)(10,15)(12,20)(13,21)(14,22)(16,29)(17,19)(18,30)(23,40)(24,36)(25,37)(26,38)(27,34)(28,39)(31,33)(32,35);(1,2)(3,6)(4,5)(7,8)(9,10,13,17)(11,19,21,15)(12,23,24,32)(14,27,26,18)(16,28,31,25)(20,35,36,40)(22,30,38,34)(29,37,33,39);(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)(78,79)(80,81)(82,83)(84,85)(86,87)

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12032, 1037917);

D47×#3127 #27084627