C₄₇×#499 #15688754

order	3008
nilpotency class	3
isoclinism	isoclinic class of #465
automorphism	?
homology	Abelianization (H₁) = C₂³×C₄₇ · Schur multiplier (H₂) = C₂

Aliases

direct product

C₄₇×#499

Subgroups

	subgroup	G/H
center, socle, prime radical	C₂²×C₄₇	C₂×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂³×C₄₇
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₄₇ ◁ C₄²×C₄₇ ◁ G

86 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

A minimal faithful permutation representation — 3 generators on 71 points:

(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47)(48,49,51,53)(50,54,55,52)(56,57,59,61)(58,64,65,71)(60,68,67,63)(62,70,69,66);(48,50,51,55)(49,52,53,54)(57,61)(62,69)(63,68)(64,71);(56,58,60,66,59,65,67,70)(57,62,63,64,61,69,68,71)

Conjugacy classes & character table

1034 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₄₇×#1363, C₄₇×#1366, C₄₇×#2228, …
maximal normal subgroup of	C₄₇×#1363, C₄₇×#1366, C₄₇×#2228, …
maximal quotient of	C₄₇×#1846, C₄₇×#1941, C₄₇×#1942, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3008, 180);

C47×#499 #15688754