D₄₇×#3552 #27123873

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

Aliases

direct product

D₄₇×#3552

Splittings

Fitting	C₄₇×#3552 ⋊ C₂
Sylow	C₄₇ ⋊ C₂×#3552

Subgroups

	subgroup	G/H
center, Frattini	C₂²	C₂⁵×D₄₇
commutator, socle, cosocle	C₂²×C₄₇	C₂⁶
Fitting	C₄₇×#3552	C₂
hypercenter	#3552	D₄₇
hypocenter	C₄₇	C₂×#3552
LCS	G ▷ C₂²×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂² ◁ #3552

7086 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)(49,52)(53,55);(48,50,51,54)(49,53,52,55)(57,63)(61,70)(62,66)(69,71);(56,59,60,68)(57,62,63,66)(58,64,65,67)(61,69,70,71);(49,52)(50,54)(56,58,60,65)(57,61,63,70)(59,67,68,64)(62,71,66,69);(48,49)(50,53)(51,52)(54,55)(56,57)(58,61)(59,66)(60,63)(62,68)(64,71)(65,70)(67,69);(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, 1077163);

D47×#3552 #27123873