D₄₇×#3538 #27123518

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

Aliases

direct product

D₄₇×#3538

Splittings

Fitting	C₄₇×#3538 ⋊ C₂
Sylow	C₄₇ ⋊ C₂×#3538

Subgroups

	subgroup	G/H
center, Frattini	C₂²	C₂⁵×D₄₇
commutator, socle, cosocle	C₂²×C₄₇	C₂⁶
Fitting	C₄₇×#3538	C₂
prime radical	#525×D₄₇	C₂
hypercenter	#3538	D₄₇
hypocenter	C₄₇	C₂×#3538
LCS	G ▷ C₂²×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂² ◁ #3538

7162 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)(56,59,60,68)(57,62,63,67)(58,66,65,71)(61,69,64,70);(49,53)(52,55)(58,65)(61,64)(66,71)(69,70);(49,53)(50,54);(48,50)(49,52)(51,54)(53,55)(56,58,60,65)(57,61,63,64)(59,66,68,71)(62,69,67,70);(48,49)(50,52)(51,53)(54,55)(56,57,60,63)(58,64,65,61)(59,67,68,62)(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

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12032, 1076808);

D47×#3538 #27123518