D₄₇×#3512 #27124773

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

Aliases

direct product

D₄₇×#3512

Splittings

Fitting	C₄₇×#3512 ⋊ C₂
Sylow	C₄₇ ⋊ C₂×#3512

Subgroups

	subgroup	G/H
center, Frattini	C₂²	C₂⁵×D₄₇
commutator, socle, cosocle	C₂²×C₄₇	C₂⁶
Fitting	C₄₇×#3512	C₂
hypercenter	#3512	D₄₇
hypocenter	C₄₇	C₂×#3512
LCS	G ▷ C₂²×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂² ◁ #3512

7238 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 71
transitive degree	μ_t(G) = 3008

A minimal faithful permutation representation — 6 generators on 71 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)(56,60,61,59)(57,64,63,69)(58,66,67,68)(62,71,65,70);(56,59,61,60)(57,64,63,69)(58,66,67,68)(62,70,65,71);(48,51,52,50)(49,53,54,55)(57,63)(62,65)(64,69)(70,71);(48,50,52,51)(49,53,54,55)(56,58,61,67)(57,62,63,65)(59,68,60,66)(64,71,69,70);(48,49)(50,53)(51,55)(52,54)(56,57)(58,65)(59,64)(60,69)(61,63)(62,67)(66,71)(68,70);(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

1100 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12032, 1078063);

D47×#3512 #27124773