D₄₇×#3515 #27124378

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

Aliases

direct product

D₄₇×#3515

Splittings

Fitting	C₄₇×#3515 ⋊ C₂
Sylow	C₄₇ ⋊ C₂×#3515

Subgroups

	subgroup	G/H
center, Frattini	C₂²	C₂⁵×D₄₇
commutator, socle, cosocle	C₂²×C₄₇	C₂⁶
Fitting	C₄₇×#3515	C₂
hypercenter	#3515	D₄₇
hypocenter	C₄₇	C₂×#3515
LCS	G ▷ C₂²×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂² ◁ #3515

7142 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)(57,63)(61,64)(62,69)(68,70);(58,66)(61,64)(65,71)(68,70);(49,52)(53,55)(56,59,60,67)(57,62,63,69)(58,65,66,71)(61,68,64,70);(56,58)(57,61)(59,65)(60,66)(62,68)(63,64)(67,71)(69,70);(48,49)(50,53)(51,52)(54,55)(56,57,60,63)(58,64,66,61)(59,62,67,69)(65,70,71,68);(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, 1077668);

D47×#3515 #27124378