C₃×C₇₁×D₄₇ #34093545

order	20022
isoclinism	isoclinic class of D₄₇
automorphism	?
homology	Abelianization (H₁) = C₂×C₃×C₇₁ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₃×C₇₁×D₄₇
unambiguous semidirect product	C₄₇⋊(C₂×C₃×C₇₁)

Splittings

Fitting, socle, Hall	C₃×C₄₇×C₇₁ ⋊ C₂
derived, Sylow	C₄₇ ⋊ C₂×C₃×C₇₁
Hall	C₄₇×C₇₁ ⋊ C₂×C₃
Hall	C₃×C₄₇ ⋊ C₂×C₇₁

Subgroups

	subgroup	G/H
center, hypercenter	C₃×C₇₁	D₄₇
commutator, cosocle, hypocenter	C₄₇	C₂×C₃×C₇₁
Frattini	C₁	G
Fitting, socle	C₃×C₄₇×C₇₁	C₂
LCS	G ▷ C₄₇
UCS	C₁ ◁ C₃×C₇₁

16 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 121
transitive degree	μ_t(G) = 10011

A minimal faithful permutation representation — 2 generators on 121 points:

(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)(48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118)(119,120,121);(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)

Conjugacy classes & character table

5325 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(20022, 3);

C3×C71×D47 #34093545