D₄₇×#3565 #27123774

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

Aliases

direct product

D₄₇×#3565

Splittings

Fitting	C₄₇×#3565 ⋊ C₂
Sylow	C₄₇ ⋊ C₂×#3565

Subgroups

	subgroup	G/H
center, Frattini	C₂²	C₂⁵×D₄₇
commutator, socle, cosocle	C₂²×C₄₇	C₂⁶
Fitting	C₄₇×#3565	C₂
hypercenter	#3565	D₄₇
hypocenter	C₄₇	C₂×#3565
LCS	G ▷ C₂²×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂² ◁ #3565

6554 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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)(64,68,69,67)(65,73,72,71)(66,75,76,77)(70,78,74,79);(48,51,52,59)(49,55,54,58)(50,57,56,62)(53,60,61,63)(65,72)(66,76)(71,73)(75,77);(49,54)(50,56)(55,58)(57,62)(64,67,69,68)(65,71,72,73)(66,75,76,77)(70,78,74,79);(48,50)(49,53)(51,57)(52,56)(54,61)(55,60)(58,63)(59,62)(64,66)(65,70)(67,77)(68,75)(69,76)(71,79)(72,74)(73,78);(48,49,52,54)(50,53,56,61)(51,58,59,55)(57,63,62,60)(64,65,69,72)(66,74,76,70)(67,73,68,71)(75,78,77,79);(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, 1077064);

D47×#3565 #27123774