D₄₇×#3486 #27124439

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

Aliases

direct product

D₄₇×#3486

Splittings

Fitting	C₄₇×#3486 ⋊ C₂
Sylow	C₄₇ ⋊ C₂×#3486

Subgroups

	subgroup	G/H
center, Frattini	C₂²	C₂⁵×D₄₇
commutator, socle, cosocle	C₂²×C₄₇	C₂⁶
Fitting	C₄₇×#3486	C₂
hypercenter	#3486	D₄₇
hypocenter	C₄₇	C₂×#3486
LCS	G ▷ C₂²×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂² ◁ #3486

11254 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)(53,59)(57,60)(58,67)(65,66);(52,55,56,64)(53,58,59,67)(54,61,62,63)(57,65,60,66);(49,51);(52,54,56,62)(53,57,59,60)(55,63,64,61)(58,66,67,65);(48,49)(50,51)(52,53)(54,60)(55,58)(56,59)(57,62)(61,66)(63,65)(64,67);(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, 1077729);

D47×#3486 #27124439