D₄₇×#3531 #27123175

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

Aliases

direct product

D₄₇×#3531

Splittings

Fitting	C₄₇×#3531 ⋊ C₂
Sylow	C₄₇ ⋊ C₂×#3531

Subgroups

	subgroup	G/H
center	C₂×C₄	C₂⁴×D₄₇
commutator, socle, cosocle	C₂²×C₄₇	C₂⁶
Frattini	C₂²	C₂⁵×D₄₇
Fitting	C₄₇×#3531	C₂
hypercenter	#3531	D₄₇
hypocenter	C₄₇	C₂×#3531
LCS	G ▷ C₂²×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂×C₄ ◁ #3531

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)(64,67,68,75)(65,71,70,77)(66,74,73,79)(69,76,72,78);(49,55)(53,62)(54,58)(61,63)(65,70)(66,73)(71,77)(74,79);(48,51,52,60)(49,54,55,58)(50,56,57,59)(53,61,62,63)(66,73)(69,72)(74,79)(76,78);(48,50,52,57)(49,53,55,62)(51,59,60,56)(54,63,58,61)(64,66)(65,69)(67,74)(68,73)(70,72)(71,76)(75,79)(77,78);(48,49)(50,53)(51,58)(52,55)(54,60)(56,63)(57,62)(59,61)(64,65)(66,72)(67,71)(68,70)(69,73)(74,78)(75,77)(76,79);(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, 1076465);

D47×#3531 #27123175