C₇×#9937 #13187153

order	1792
nilpotency class	3
isoclinism	isoclinic class of #9930
automorphism	?
homology	Abelianization (H₁) = C₂³×C₇ · Schur multiplier (H₂) = C₂³

Aliases

direct product

C₇×#9937

Subgroups

	subgroup	G/H
center, socle	C₂²×C₇	#392
commutator, Frattini, cosocle	C₂³×C₄	C₂³×C₇
prime radical	C₂⁴×C₇	C₂×D₄
LCS	G ▷ C₂³×C₄ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₇ ◁ C₂³×C₄×C₇ ◁ G

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

normal subgroups only

This group has 526 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) = 39
transitive degree	μ_t(G) = 448

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

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

Conjugacy classes & character table

217 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1792, 2925);