D₄₇×#3290 #27092480

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

Aliases

direct product

D₄₇×#3290

Splittings

Fitting	C₄₇×#3290 ⋊ C₂
Sylow	C₄₇ ⋊ C₂×#3290

Subgroups

	subgroup	G/H
center	C₂	D₄²×D₄₇
commutator, cosocle	C₂×C₄×C₄₇	C₂⁵
Frattini	C₂×C₄	C₂⁴×D₄₇
Fitting	C₄₇×#3290	C₂
socle	C₂×C₄₇	C₂×D₄²
hypercenter	#3290	D₄₇
hypocenter	C₄₇	C₂×#3290
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ #3290

2650 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 79
transitive degree	μ_t(G) = 1504

A minimal faithful permutation representation — 5 generators on 79 points:

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

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, 1045770);

D47×#3290 #27092480