D₄₇×#3563 #27123648

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

Aliases

direct product

D₄₇×#3563

Splittings

Fitting	C₄₇×#3563 ⋊ C₂
Sylow	C₄₇ ⋊ C₂×#3563

Subgroups

	subgroup	G/H
center, Frattini	C₂²	C₂⁵×D₄₇
commutator, socle, cosocle	C₂²×C₄₇	C₂⁶
Fitting	C₄₇×#3563	C₂
prime radical	#121×D₄₇	C₂²
hypercenter	#3563	D₄₇
hypocenter	C₄₇	C₂×#3563
LCS	G ▷ C₂²×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂² ◁ #3563

6458 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)(49,55)(53,56)(54,61)(60,62);(50,58)(53,56)(57,63)(60,62)(64,67,68,75)(65,71,70,74)(66,73,72,78)(69,76,77,79);(48,51,52,59)(49,54,55,61)(50,57,58,63)(53,60,56,62)(65,70)(66,72)(71,74)(73,78);(48,50,52,58)(49,53,55,56)(51,57,59,63)(54,60,61,62)(64,66)(65,69)(67,73)(68,72)(70,77)(71,76)(74,79)(75,78);(48,49)(50,56)(51,54)(52,55)(53,58)(57,62)(59,61)(60,63)(64,65,68,70)(66,69,72,77)(67,74,75,71)(73,79,78,76);(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, 1076938);

D47×#3563 #27123648