D₄₇×#3568 #27123704

order	12032
automorphism	?
homology	Abelianization (H₁) = C₂⁶ · Schur multiplier (H₂) = C₂¹³

Aliases

direct product

D₄₇×#3568

Splittings

Fitting	C₄₇×#3568 ⋊ C₂
Sylow	C₄₇ ⋊ C₂×#3568

Subgroups

	subgroup	G/H
center, Frattini	C₂²	C₂⁵×D₄₇
commutator, socle, cosocle	C₂²×C₄₇	C₂⁶
Fitting	C₄₇×#3568	C₂
hypercenter	#3568	D₄₇
hypocenter	C₄₇	C₂×#3568
LCS	G ▷ C₂²×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂² ◁ #3568

6726 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

A minimal faithful permutation representation — 6 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)(54,59)(62,63)(64,68,69,67)(65,72,71,76)(66,75,73,74)(70,77,78,79);(49,55)(50,58)(54,59)(57,60)(64,67,69,68)(65,72,71,76)(66,74,73,75)(70,77,78,79);(48,51,52,61)(49,54,55,59)(50,57,58,60)(53,62,56,63)(65,71)(66,73)(72,76)(74,75);(48,50)(49,53)(51,60)(52,58)(54,63)(55,56)(57,61)(59,62)(64,66)(65,70)(67,74)(68,75)(69,73)(71,78)(72,77)(76,79);(48,49,52,55)(50,56,58,53)(51,59,61,54)(57,62,60,63)(64,65)(66,70)(67,76)(68,72)(69,71)(73,78)(74,79)(75,77);(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, 1076994);

D47×#3568 #27123704