D₄₇×#3119 #27084517

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

Aliases

direct product

D₄₇×#3119

Splittings

Fitting	C₄₇×#3119 ⋊ C₂
Sylow	C₄₇ ⋊ C₂×#3119

Subgroups

	subgroup	G/H
center	C₂²	C₂²×D₄×D₄₇
commutator, cosocle	C₂×C₄×C₄₇	C₂⁵
Frattini	C₂×C₄	C₂⁴×D₄₇
Fitting	C₄₇×#3119	C₂
socle	C₂²×C₄₇	C₂³×D₄
hypercenter	#3119	D₄₇
hypocenter	C₄₇	C₂×#3119
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂² ◁ #117 ◁ #3119

2198 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 71
transitive degree	μ_t(G) = 3008

A minimal faithful permutation representation — 5 generators on 71 points:

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

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, 1037807);

D47×#3119 #27084517