D₄₇×#3541 #27123427

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

Aliases

direct product

D₄₇×#3541

Splittings

Fitting	C₄₇×#3541 ⋊ C₂
Sylow	C₄₇ ⋊ C₂×#3541

Subgroups

	subgroup	G/H
center, Frattini	C₂²	C₂⁵×D₄₇
commutator, socle, cosocle	C₂²×C₄₇	C₂⁶
Fitting	C₄₇×#3541	C₂
hypercenter	#3541	D₄₇
hypocenter	C₄₇	C₂×#3541
LCS	G ▷ C₂²×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂² ◁ #3541

7258 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)(57,63,64,69)(58,66,67,68)(62,71,65,70);(49,53)(52,55)(56,59,61,60)(57,63,64,69)(58,66,67,68)(62,70,65,71);(49,53)(50,54);(48,50)(49,52)(51,54)(53,55)(56,58)(57,62)(59,68)(60,66)(61,67)(63,71)(64,65)(69,70);(48,49)(50,52)(51,53)(54,55)(56,57)(58,65)(59,63)(60,69)(61,64)(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

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12032, 1076717);

D47×#3541 #27123427