D₄₇×#3131 #27085476

order	12032
automorphism	?
homology	Abelianization (H₁) = C₂⁵ · Schur multiplier (H₂) = C₂⁷×C₄

Aliases

direct product

D₄₇×#3131

Splittings

Fitting	C₄₇×#3131 ⋊ C₂
Sylow	C₄₇ ⋊ C₂×#3131

Subgroups

	subgroup	G/H
center	C₂×C₄	C₂×D₄×D₄₇
commutator, cosocle	C₂×C₄×C₄₇	C₂⁵
Frattini	C₂×C₄	C₂⁴×D₄₇
Fitting	C₄₇×#3131	C₂
socle	C₂²×C₄₇	C₂³×D₄
prime radical	#532×D₄₇	C₂
hypercenter	#3131	D₄₇
hypocenter	C₄₇	C₂×#3131
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #3131

2222 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:

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

1100 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12032, 1038766);

D47×#3131 #27085476