D₄₇×#2981 #27081056

order	12032
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₄ · Schur multiplier (H₂) = C₂⁸

Aliases

direct product

D₄₇×#2981

Splittings

Fitting	C₄₇×#2981 ⋊ C₂
Sylow	C₄₇ ⋊ C₂×#2981

Subgroups

	subgroup	G/H
center, Frattini	C₂×C₄	C₂⁴×D₄₇
commutator, socle	C₂²×C₄₇	C₂⁴×C₄
Fitting	C₄₇×#2981	C₂
prime radical	#532×D₄₇	C₂
cosocle	C₂×C₄×C₄₇	C₂⁵
hypercenter	#2981	D₄₇
hypocenter	C₄₇	C₂×#2981
LCS	G ▷ C₂²×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂×C₄ ◁ #2981

2230 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 71
transitive degree	μ_t(G) = 3008

A minimal faithful permutation representation — 5 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)(49,53)(52,54)(56,58)(57,62)(59,65)(60,66)(61,64)(63,70)(67,69)(68,71);(50,55)(52,54)(58,65)(62,64)(66,69)(70,71);(48,50)(49,52)(51,55)(53,54)(57,61)(58,65)(63,68)(66,69);(48,49)(50,54)(51,53)(52,55)(56,57,60,63,59,61,67,68)(58,64,66,71,65,62,69,70);(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

1100 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12032, 1034346);

D47×#2981 #27081056