D₄₇×#3562 #27123750

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

Aliases

direct product

D₄₇×#3562

Splittings

Fitting	C₄₇×#3562 ⋊ C₂
Sylow	C₄₇ ⋊ C₂×#3562

Subgroups

	subgroup	G/H
center, Frattini	C₂²	C₂⁵×D₄₇
commutator, socle, cosocle	C₂²×C₄₇	C₂⁶
Fitting	C₄₇×#3562	C₂
hypercenter	#3562	D₄₇
hypocenter	C₄₇	C₂×#3562
LCS	G ▷ C₂²×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂² ◁ #3562

7354 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 71
transitive degree	μ_t(G) = 1504

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)(57,65,64,63)(58,67,68,69)(62,70,66,71);(48,50,51,54)(49,53,52,55)(57,64)(58,68)(63,65)(67,69);(48,49)(50,53)(51,52)(54,55)(56,59,61,60)(57,63,64,65)(58,67,68,69)(62,70,66,71);(49,52)(53,55)(56,58)(57,62)(59,69)(60,67)(61,68)(63,71)(64,66)(65,70);(49,52)(50,54)(56,57)(58,66)(59,65)(60,63)(61,64)(62,68)(67,70)(69,71);(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, 1077040);

D47×#3562 #27123750