C₇×#1721 #11730190

order	896
nilpotency class	3
isoclinism	isoclinic class of #1714
automorphism	?
homology	Abelianization (H₁) = C₂³×C₇ · Schur multiplier (H₂) = C₂×C₈

Aliases

	subgroup	G/H
center, socle	C₂²×C₇	#127
commutator, Frattini, cosocle	C₄²	C₂³×C₇
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₇ ◁ C₄²×C₇ ◁ G

242 conjugacy classes of subgroups; only the 80 normal subgroups are shown.

normal subgroups only

This group has 242 conjugacy classes of subgroups — too many to draw. Only its 80 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) = 448

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

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(896, 4956);