C₇×#9936 #13187152

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

Aliases

direct product

C₇×#9936

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

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

normal subgroups only

This group has 568 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)(8,9,13,17)(10,18,20,23)(11,16,12,15)(14,21,22,19)(24,25)(26,29)(27,30)(28,31)(32,35)(33,36)(34,38)(37,39);(8,10)(9,14)(11,21)(12,19)(13,20)(15,23)(16,18)(17,22)(24,26,28,33)(25,29,31,36)(27,32,34,39)(30,37,38,35);(8,10)(9,14)(11,19)(12,21)(13,20)(15,18)(16,23)(17,22)(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, 2924);