C₇×#9984 #13187200

order	1792
nilpotency class	3
isoclinism	isoclinic class of #9980
automorphism	?
homology	Abelianization (H₁) = C₂³×C₇ · Schur multiplier (H₂) = C₂³

Aliases

direct product

C₇×#9984

Subgroups

	subgroup	G/H
center, socle	C₂²×C₇	#392
commutator, Frattini, cosocle	C₂³×C₄	C₂³×C₇
prime radical	C₂×C₇×#121	C₂²
LCS	G ▷ C₂³×C₄ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₇ ◁ C₂³×C₄×C₇ ◁ G

544 conjugacy classes of subgroups; only the 98 normal subgroups are shown.

normal subgroups only

This group has 544 conjugacy classes of subgroups — too many to draw. Only its 98 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) = 39
transitive degree	μ_t(G) = 448

A minimal faithful permutation representation — 3 generators on 39 points:

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

Conjugacy classes & character table

196 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1792, 2972);