C₇×#10643 #13187859

order	1792
nilpotency class	3
isoclinism	isoclinic class of #10637
automorphism	?
homology	Abelianization (H₁) = C₂³×C₇ · Schur multiplier (H₂) = C₂²

Aliases

direct product

C₇×#10643

Subgroups

	subgroup	G/H
center, socle	C₂²×C₇	#397
commutator, Frattini, cosocle	C₂×C₄²	C₂³×C₇
prime radical	C₂³×C₇	#123
LCS	G ▷ C₂×C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₇ ◁ C₂×C₄²×C₇ ◁ G

298 conjugacy classes of subgroups; only the 102 normal subgroups are shown.

normal subgroups only

This group has 298 conjugacy classes of subgroups — too many to draw. Only its 102 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Full subgroup data →

Presentation

minimal degree	μ(G) = 47
transitive degree	μ_t(G) = 448

A minimal faithful permutation representation — 3 generators on 47 points:

(1,2,3,4,5,6,7)(8,9,12,13,11,15,10,14)(16,17)(18,26,29,39)(19,23)(20,24)(21,25)(22,28,36,33)(27,42,30,41)(31,37)(32,38)(34,40)(35,44,46,43)(45,47);(16,18,21,29)(17,22,25,36)(19,30,32,27)(20,33,34,28)(23,35,38,46)(24,39,40,26)(31,43,45,44)(37,42,47,41);(9,13)(10,12)(14,15)(16,19,20,31,21,32,34,45)(17,23,24,37,25,38,40,47)(18,27,28,43,29,30,33,44)(22,35,26,41,36,46,39,42)

Conjugacy classes & character table

259 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1792, 3631);