D₄₇×#3523 #27124491

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

Aliases

direct product

D₄₇×#3523

Splittings

Fitting	C₄₇×#3523 ⋊ C₂
Sylow	C₄₇ ⋊ C₂×#3523

Subgroups

	subgroup	G/H
center, Frattini	C₂²	C₂⁵×D₄₇
commutator, socle, cosocle	C₂²×C₄₇	C₂⁶
Fitting	C₄₇×#3523	C₂
prime radical	#121×D₄₇	C₂²
hypercenter	#3523	D₄₇
hypocenter	C₄₇	C₂×#3523
LCS	G ▷ C₂²×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂² ◁ #3523

7022 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)(48,50,51,54)(49,53,52,55)(57,62)(61,64)(63,70)(69,71);(56,59,60,68)(57,63,62,70)(58,65,66,67)(61,69,64,71);(49,52)(53,55)(57,62)(61,64)(63,70)(69,71);(56,58,60,66)(57,61,62,64)(59,67,68,65)(63,71,70,69);(48,49)(50,53)(51,52)(54,55)(56,57,60,62)(58,64,66,61)(59,63,68,70)(65,71,67,69);(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, 1077781);

D47×#3523 #27124491