D₄₇×#3500 #27124742

order	12032
automorphism	?
homology	Abelianization (H₁) = C₂⁶ · Schur multiplier (H₂) = C₂¹⁴

Aliases

direct product

D₄₇×#3500

Splittings

Fitting	C₄₇×#3500 ⋊ C₂
Sylow	C₄₇ ⋊ C₂×#3500

Subgroups

	subgroup	G/H
center, Frattini	C₂²	C₂⁵×D₄₇
commutator, socle, cosocle	C₂²×C₄₇	C₂⁶
Fitting	C₄₇×#3500	C₂
hypercenter	#3500	D₄₇
hypocenter	C₄₇	C₂×#3500
LCS	G ▷ C₂²×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂² ◁ #3500

11534 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 67
transitive degree	μ_t(G) = 1504

A minimal faithful permutation representation — 6 generators on 67 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)(52,55,56,64)(53,59,58,63)(54,62,61,67)(57,65,60,66);(54,61)(57,60)(62,67)(65,66);(48,49,50,51)(53,58)(57,60)(59,63)(65,66);(52,54)(53,57)(55,62)(56,61)(58,60)(59,65)(63,66)(64,67);(49,51)(52,53)(54,60)(55,63)(56,58)(57,61)(59,64)(62,65)(66,67);(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, 1078032);

D47×#3500 #27124742