C₇×#2029 #11730498

order	896
nilpotency class	3
isoclinism	isoclinic class of #2021
automorphism	?
homology	Abelianization (H₁) = C₂³×C₇ · Schur multiplier (H₂) = C₂⁴

Aliases

	subgroup	G/H
center, socle	C₂²×C₇	#120
commutator, Frattini, cosocle	C₂⁴	C₂³×C₇
prime radical	C₂⁵×C₇	C₂²
LCS	G ▷ C₂⁴ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₇ ◁ C₂⁴×C₇ ◁ G

466 conjugacy classes of subgroups; only the 84 normal subgroups are shown.

normal subgroups only

This group has 466 conjugacy classes of subgroups — too many to draw. Only its 84 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) = 112

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

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(896, 5264);