C₇×#2537 #11741846

order	896
nilpotency class	2
isoclinism	isoclinic class of #2403
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₇ · Schur multiplier (H₂) = C₂⁶

Aliases

	subgroup	G/H
center, socle	C₂³×C₇	C₂⁴
commutator, Frattini, cosocle	C₂³	C₂⁴×C₇
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂³×C₇ ◁ G

788 conjugacy classes of subgroups; only the 248 normal subgroups are shown.

normal subgroups only

This group has 788 conjugacy classes of subgroups — too many to draw. Only its 248 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

minimal degree	μ(G) = 19
transitive degree	μ_t(G) = 448

A minimal faithful permutation representation — 4 generators on 19 points:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(896, 16612);