C₇×#9482 #13186698

order	1792
nilpotency class	3
isoclinism	isoclinic class of #9471
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₇ · Schur multiplier (H₂) = C₂³

Aliases

direct product

C₇×#9482

Subgroups

	subgroup	G/H
center, socle	C₂²×C₇	#386
commutator	C₂²×C₄	C₂²×C₄×C₇
Frattini, cosocle	C₂³×C₄	C₂³×C₇
prime radical	C₂⁴×C₇	C₂×D₄
LCS	G ▷ C₂²×C₄ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₇ ◁ C₂³×C₄×C₇ ◁ G

518 conjugacy classes of subgroups; only the 122 normal subgroups are shown.

normal subgroups only

This group has 518 conjugacy classes of subgroups — too many to draw. Only its 122 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)(8,9,12,16,13,17,11,15)(10,18,19,22,21,23,20,14)(24,25)(26,29)(27,34,35,30)(28,31)(32,36,38,39)(33,37);(8,10)(9,14,17,22)(11,20)(12,19)(13,21)(15,23,16,18)(24,26,28,33)(25,29,31,37)(27,32,35,38)(30,36,34,39);(8,11,13,12)(9,15,17,16)(10,19,21,20)(14,18,22,23)(24,27)(25,30)(26,32)(28,35)(29,36)(31,34)(33,38)(37,39)

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, 2470);