D₄₇×#3504 #27124752

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

Aliases

direct product

D₄₇×#3504

Splittings

Fitting	C₄₇×#3504 ⋊ C₂
Sylow	C₄₇ ⋊ C₂×#3504

Subgroups

	subgroup	G/H
center, Frattini	C₂²	C₂⁵×D₄₇
commutator, socle, cosocle	C₂²×C₄₇	C₂⁶
Fitting	C₄₇×#3504	C₂
prime radical	C₂×#41×D₄₇	C₂²
hypercenter	#3504	D₄₇
hypocenter	C₄₇	C₂×#3504
LCS	G ▷ C₂²×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂² ◁ #3504

6958 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)(56,59,60,68)(57,63,62,67)(58,66,65,71)(61,69,64,70);(58,65)(61,64)(66,71)(69,70);(48,50,51,55)(49,52,53,54)(57,62)(61,64)(63,67)(69,70);(56,58)(57,61)(59,66)(60,65)(62,64)(63,69)(67,70)(68,71);(48,49,51,53)(50,54,55,52)(56,57,60,62)(58,64,65,61)(59,67,68,63)(66,69,71,70);(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, 1078042);

D47×#3504 #27124752