D₄₇×#3316 #27092860

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

Aliases

direct product

D₄₇×#3316

Splittings

Fitting	C₄₇×#3316 ⋊ C₂
Sylow	C₄₇ ⋊ C₂×#3316

Subgroups

	subgroup	G/H
center	C₂²	C₂²×D₄×D₄₇
commutator, cosocle	C₂×C₄×C₄₇	C₂⁵
Frattini	C₂×C₄	C₂⁴×D₄₇
Fitting	C₄₇×#3316	C₂
socle	C₂²×C₄₇	C₂³×D₄
prime radical	#548×D₄₇	C₂
hypercenter	#3316	D₄₇
hypocenter	C₄₇	C₂×#3316
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂² ◁ C₄×D₄ ◁ #3316

2158 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:

(3,8)(5,7)(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);(9,11,13,18)(10,14,16,23)(12,21,22,19)(15,24,20,17);(1,3)(2,5)(4,8)(6,7)(11,18)(14,23)(17,24)(19,21);(1,2,4,6)(3,7,8,5)(9,10,13,16)(11,17,18,24)(12,20,22,15)(14,21,23,19);(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

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12032, 1046150);

D47×#3316 #27092860