D₄₇×#2987 #27081243

order	12032
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₄ · Schur multiplier (H₂) = C₂⁸

Aliases

direct product

D₄₇×#2987

Splittings

Fitting	C₄₇×#2987 ⋊ C₂
Sylow	C₄₇ ⋊ C₂×#2987

Subgroups

	subgroup	G/H
center, Frattini	C₂×C₄	C₂⁴×D₄₇
commutator, socle	C₂²×C₄₇	C₂⁴×C₄
Fitting	C₄₇×#2987	C₂
prime radical	C₂³×D₄₇	C₂²×C₄
cosocle	C₂×C₄×C₄₇	C₂⁵
hypercenter	#2987	D₄₇
hypocenter	C₄₇	C₂×#2987
LCS	G ▷ C₂²×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂×C₄ ◁ #2987

1706 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 79
transitive degree	μ_t(G) = 3008

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

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

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12032, 1034533);

D47×#2987 #27081243