C₇³×C₄₇ #30633170

order	16121
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	?
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₇³

Aliases

abelian

C₇³×C₄₇

Subgroups

	subgroup	G/H
center	G	C₁
commutator, Frattini	C₁	G
LCS	G ▷ C₁
UCS	C₁ ◁ G

232 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 68
transitive degree	μ_t(G) = 16121

A minimal faithful permutation representation — 3 generators on 68 points:

(1,2,3,4,5,6,7)(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);(8,9,10,11,12,13,14);(15,16,17,18,19,20,21)

Conjugacy classes & character table

16121 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₂×C₇³×C₄₇
maximal normal subgroup of	C₂×C₇³×C₄₇
maximal quotient of	C₂×C₇³×C₄₇

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(16121, 5);

C73×C47 #30633170