C₇×#10088 #13187304

order	1792
nilpotency class	3
isoclinism	isoclinic class of #10088
automorphism	?
homology	Abelianization (H₁) = C₂³×C₇ · Schur multiplier (H₂) = C₂²×C₄

Aliases

	subgroup	G/H
center, socle	C₂²×C₇	#392
commutator, Frattini, cosocle	C₂×C₄²	C₂³×C₇
LCS	G ▷ C₂×C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₇ ◁ C₂×C₄²×C₇ ◁ G

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

normal subgroups only

This group has 770 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.

minimal degree	μ(G) = 23
transitive degree	μ_t(G) = 224

A minimal faithful permutation representation — 3 generators on 23 points:

(1,2,3,4,5,6,7)(8,9)(10,12)(11,14)(13,15)(17,20)(18,22)(21,23);(9,12)(10,15)(13,14)(18,22)(20,23);(10,15)(12,13)(16,17)(18,23)(19,21)(20,22)

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1792, 3076);