C₇×#3496 #11744448

order	896
nilpotency class	2
isoclinism	isoclinic class of #3484
automorphism	?
homology	Abelianization (H₁) = C₂⁵×C₇ · Schur multiplier (H₂) = C₂⁹

Aliases

	subgroup	G/H
center, socle	C₂²×C₇	C₂⁵
commutator, Frattini, cosocle	C₂²	C₂⁵×C₇
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₇ ◁ G

1660 conjugacy classes of subgroups.

minimal degree	μ(G) = 19
transitive degree	μ_t(G) = 224

A minimal faithful permutation representation — 5 generators on 19 points:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(896, 19214);