D₄₇×#3040 #27083136

order	12032
automorphism	?
homology	Abelianization (H₁) = C₂⁵ · Schur multiplier (H₂) = C₂⁹

Aliases

direct product

D₄₇×#3040

Splittings

Fitting	C₄₇×#3040 ⋊ C₂
Sylow	C₄₇ ⋊ C₂×#3040

Subgroups

	subgroup	G/H
center	C₂²	C₂²×D₄×D₄₇
commutator, cosocle	C₂×C₄×C₄₇	C₂⁵
Frattini	C₂×C₄	C₂⁴×D₄₇
Fitting	C₄₇×#3040	C₂
socle	C₂²×C₄₇	C₂³×D₄
prime radical	C₂×AGL(1,ℤ/8)×D₄₇	C₂
hypercenter	#3040	D₄₇
hypocenter	C₄₇	C₂×#3040
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ #3040

2918 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 67
transitive degree	μ_t(G) = 1504

A minimal faithful permutation representation — 5 generators on 67 points:

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

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, 1036426);

D47×#3040 #27083136