C₄₇×#488 #15688743

order	3008
nilpotency class	3
isoclinism	isoclinic class of #465
automorphism	?
homology	Abelianization (H₁) = C₂³×C₄₇ · Schur multiplier (H₂) = C₄

Aliases

direct product

C₄₇×#488

Subgroups

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

96 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 71
transitive degree	μ_t(G) = 1504

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

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₄₇×#1414, C₂×C₄₇×#488, C₄₇×#3131, …
maximal normal subgroup of	C₄₇×#1414, C₂×C₄₇×#488, C₄₇×#3131, …
maximal quotient of	C₄₇×#1835, C₄₇×#1933, C₄₇×#1934, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3008, 169);

C47×#488 #15688743